
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
Given triangle \( \triangle ABC \) with midpoint \( N \) of side \( AB \), where \( \angle A > \angle B \). Point \( D \) lies on ray \( AC \) such that \( CD = BC \). Point \( P \) lies on ray \( DN \) on the same side of \( BC \) as point \( A \), such that \( \angle PBC = \angle A \). Segment \( PC \) intersects \( AB \) at point \( E \) and segment \( DP \) intersects \( BC \) at point \( T \). Find the value of the expression \( \frac{BC}{TC} - \frac{EA}{EB} \).

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