
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 the square \(ABCD\), points \(E\) and \(F\) are on sides \(AD\) and \(BC\) respectively, such that \(EF \parallel AB\). Points \(G\) and \(H\) are on sides \(AB\) and \(DC\) respectively, such that \(GH \parallel AD\). \(EF\) and \(GH\) intersect at point \(K\). If the area of rectangle \(KFCH\) is twice the area of rectangle \(AGKE\), find the degree measure of \(\angle FAH\).

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