By Tom Westbrook, Elizabeth Howcroft and Chibuike Oguh

NEW YORK/SINGAPORE/PARIS (Reuters) -Bitcoin, the world’s largest cryptocurrency, approached the previous session’s record high on Tuesday in choppy trading as the top U.S. markets regulator unveiled a plan to overhaul rules for the sector.

Bitcoin hit a record high $109,071 on Monday when Trump, who has pledged to be a “crypto president,” was sworn in, but sank when crypto was not included in a flurry of executive actions on Day One.

Bitcoin prices rose 3.8% while Ethereum , the second-largest cryptocurrency, gained 1.4% as the market shook off some of that disappointment.

The Securities and Exchange Commission’s new leadership said on Tuesday it had created a task force to…