
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 $x^{10} = a + a_{1}(x-1) + a_{2}(x-1)^{2} + \ldots + a_{10}(x-1)^{10}$ ($a, a_{1}, \ldots, a_{10} \in \mathbb{R}$), then find $a_{1}$.

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