
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
Each flatbread, regardless of its shape, can be divided into four equal parts by two mutually perpendicular cuts. In other words, for any planar region with area \( P \), one can find two mutually perpendicular lines such that each of the four quarters they create contains a part of the region with area \( P / 4 \).

(Proving this theorem is significantly easier than actually splitting, say, a triangle with sides \( 3, 4, 5 \) into four equal parts.)

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