
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
Given a natural number \( n \), the polynomial
\[ P(x) = \sum_{h=0}^{n} \binom{n}{h} x^{n-h}(x-1)^{h} \]
can be expanded into an ascending order of \( x \) as \( a_{0} + a_{1} x + a_{2} x^{2} + \cdots + a_{n} x^{n} \). Find
\[ \left| a_{0} \right| + \left| a_{1} \right| + \left| a_{2} \right| + \cdots + \left| a_{n} \right|. \]

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