
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
The graph of the function \( f(x) = x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0 \) (where \( n > 1 \)), intersects the line \( y = b \) at the points \( B_1, B_2, \ldots, B_n \) (from left to right), and the line \( y = c \) (\( c \neq b \)) at the points \( C_1, C_2, \ldots, C_n \) (from left to right). Let \( P \) be a point on the line \( y = c \), to the right of the point \( C_n \). Find the sum \( \cot \angle B_1 C_1 P + \cdots + \cot \angle B_n C_n P \).

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