
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
There is a rectangular field that measures  $20\text{m}$  by  $15\text{m}$ . Xiaoyu the butterfly is sitting at the perimeter of the field on one of the  $20\text{m}$  sides such that he is  $6\text{m}$  from a corner. He flies in a straight line to another point on the perimeter. His flying path splits the field into two parts with equal area. How far in meters did Xiaoyu fly?

Present the answer in LaTex format: \boxed{Your answer}
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