By Amanda Cooper LONDON (Reuters) -The pound hit its highest since mid-September on Tuesday, as investor gloom over Britain’s economic outlook was temporarily offset by a glimmer of optimism over Rishi Sunak taking over as prime minister. The 42-year-old former finance minister is now Britain’s third prime minister in less than two months. Sunak said on Tuesday he would try to fix the mess left by his predecessor, restore trust in British politics and tackle a “profound economic crisis” but warned the country there would be difficult decisions. Jeremy Hunt, who outgoing Prime Minister Liz Trus…