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By Alex Lawler LONDON (Reuters) - OPEC's oil output rose in April to close to the highest level in recent history, a Reuters survey found on Friday, as production increases led by Iran and Iraq more than offset a strike in Kuwait and other outages. Top exporter Saudi Arabia, however, made no major change to output, the survey found, despite the kingdom hinting it could boost supply after OPEC and non-member nations failed to agree to freeze output at a meeting on April 17. "This rally doesn't have strong legs." Supply from the Organization of the Petroleum Exporting Countries rose to 32.64 million barrels per day (bpd) this month, from 32.47 million bpd in March, according to the survey, based on shipping data and information from sources at oil companies, OPEC and consultants.