
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
Let \(ABCD\) be a rectangle with \(BC = 2 \cdot AB\). Let \(E\) be the midpoint of \(BC\) and \(P\) an arbitrary point on the side \(AD\). Let \(F\) and \(G\) be the feet of the perpendiculars drawn from \(A\) to \(BP\) and from \(D\) to \(CP\), respectively. It is known that \(\angle BPC = 85^{\circ}\).

a) Verify that the triangles \(BEF\) and \(BEP\) are similar.

b) Determine the value of the sum of the angles \(\angle BEF + \angle CEG\).

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