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* Britain's Next shines on profit forecast hike

* Adidas, Puma slip after JD Sports warns on profit

* Euro zone business activity shrank again in Dec

* Inflation up in German states, France in Dec

Jan 4 (Reuters) - European shares bounced back on Thursday, boosted by healthcare and energy stocks, with adamant investors assessing a slew of economic data for any signs that the European Central Bank could loosen monetary policy sooner than expected this year.

The pan-European STOXX 600 was up 0.4% by 0917 GMT, after falling for two straight days and touching a three-week low in the previous session.

Sentiment was also boosted by data showing China's services activity expanded at the fastest pace in five months.

"There is a lot of risk appetite left for European equities and this rebound we're seeing could last a little bit longer," said Anthi Tsouvali, multi-asset strategist at State Street Global Markets.

All eyes are on whether the previous year's rally, broadly built on the back of escalating bets of interest rate cuts, will extend into 2024. However, that has also made stocks overvalued, say analysts, capping their potential for further sharp gains.

"European equities would lag other markets also because of their cyclicality and risks like higher-for-longer rates, dependency on manufacturing, and ongoing geopolitical risks," Tsouvali added.

Meanwhile, data showing rising inflation in German states and France is complicating the ECB's job at a time when the bloc's economy seems to be in recession, with fresh data showing the contraction in euro zone business activity continued at the end of 2023.

So far, slowing inflation and economic downturn had spurred bets of rate cuts heading into 2024.

The data came a day after the minutes of the U.S. Federal Reserve's December policy meeting showed a growing sense that inflation is under control and rising concerns about economic risks from a restrictive monetary policy.

Energy was the top sector gainer, up 1.2% on higher oil prices, with Norway's Equinor leading the gains.

Healthcare, too rose 1%, led by a near 3% rise in Novo Nordisk.

British clothing retailer Next jumped 4.7%, hitting a record high and topping the STOXX 600 after raising its profit forecast for its current fiscal year.

Evotec slumped 20% and was on track for its worst one-day drop since October 2002 after the German biotechnology firm announced the "surprising" departure of its long-term CEO.

The German DAX was up 0.3%, with losses in sportswear firm Adidas capping the index's gains. Both Adidas and Puma dropped over 3% each after British rival JD Sports Fashion lowered its full-year profit forecast. JD Sports tumbled 22.1%.

Aixtron lost 4.5% after UBS initiated coverage on the German chip systems manufacturer's stock with a "sell" rating, while BE Semiconductor Industries fell 3.4% after the same brokerage downgraded it to "neutral" from "buy". (Reporting by Ankika Biswas in Bengaluru; Editing by Sohini Goswami)