
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 an isosceles triangle \(ABC\), the base \(BC\) is \(\frac{1}{4}\) of the perimeter. From any point \(P\) on the base \(BC\), draw a line parallel to the two legs, intersecting the legs at points \(E\) and \(F\), respectively. Find the ratio of the perimeter of quadrilateral \(AEPF\) to the perimeter of \(\triangle ABC\).

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