
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
Square $EFGH$ has sides of length 4. A point $P$ on $EH$ is such that line segments $FP$ and $GP$ divide the square’s area into four equal parts. Find the length of segment $FP$.
A) $2\sqrt{3}$
B) $3$
C) $2\sqrt{5}$
D) $4$
E) $2\sqrt{7}$

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