
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
Factor the polynomial \(x^{10} - 1\) into non-constant polynomials with real coefficients to determine the maximum number \(k\) of such factors:
\[x^{10} - 1 = q_1(x) q_2(x) \dotsm q_k(x).\]
What is the largest possible value of \(k\)?

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