
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

In rectangle \(A B C D\), point \(E\) is the midpoint of side \(C D\). On side \(B C\), point \(F\) is chosen such that \(\angle A E F\) is a right angle. Find the length of segment \(F C\) if \(A F = 7\) and \(B F = 4\).

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