
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 that $a, \theta \in \mathbb{R}$ and $m \in \mathbb{N}$, and the polynomial \( P(x) = x^{2m} - 2|a|^{m} x^{m} \cos \theta + a^{2m} \), factorize \( P(x) \) as a product of \( m \) real quadratic polynomials.

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