
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  $f(x)=x^n+a_{n-1}x_{n-1}+\ldots +a_1x+a_0$  (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  $y=c\ (c\not= b)$  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 to the point  $C_n$ . Find the sum
\[\cot (\angle B_1C_1P)+\ldots +\cot (\angle B_nC_nP) \]

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