
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  $p(x)$  be a polynomial of degree 4 with leading coefficients 1. Suppose  $p(1)=1$ ,  $p(2)=2$ ,  $p(3)=3$ ,  $p(4)=4$ . Then  $p(5)=$ [list=1]
[*] 5
[*]  $\frac{25}{6}$ [*] 29
[*] 35
[/list]

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