
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 rectangle \(ABCD\) (with \(AB \parallel CD\)), a triangle \(AEF\) is inscribed. Point \(E\) lies on side \(BC\), and point \(F\) lies on side \(CD\). Find the tangent of the angle \(EAF\) if \(\frac{AB}{BC} = \frac{BE}{EC} = \frac{CF}{FD} = k\).

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