
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  $P(x) = x^3 - 6x^2 - 5x + 4$ . Suppose that  $y$  and  $z$  are real numbers such that
 \[ zP(y) = P(y - n) + P(y + n) \]
for all reals  $n$ . Evaluate  $P(y)$ .

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