
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
When Cirno walks into her perfect math class today, she sees a polynomial  $P(x)=1$  (of degree 0) on the blackboard. As her teacher explains, for her pop quiz today, she will have to perform one of the two actions every minute:

(a) Add a monomial to  $P(x)$  so that the degree of  $P$  increases by 1 and  $P$  remains monic;
(b) Replace the current polynomial  $P(x)$  by  $P(x+1)$ . For example, if the current polynomial is  $x^2+2x+3$ , then she will change it to  $(x+1)^2+2(x+1)+3=x^2+4x+6$ .

Her score for the pop quiz is the sum of coefficients of the polynomial at the end of 9 minutes. Given that Cirno (miraculously) doesn't make any mistakes in performing the actions, what is the maximum score that she can get?

*Proposed by Yannick Yao*

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