
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
If $x + x^2 + x^3 + \ldots + x^9 + x^{10} = a_0 + a_1(1 + x) + a_2(1 + x)^2 + \ldots + a_9(1 + x)^9 + a_{10}(1 + x)^{10}$, then $a_9 = \_\_\_\_\_\_\_\_$.

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