
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
Find the maximum number of real roots for the polynomial
\[x^n + x^{n-1} + \dots + x^2 + x + c = 0,\] where $n$ is a positive integer and $c$ is a real constant different from 1.

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