
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 to a polynomial of the form
\[x^n + x^{n - 1} + \dots + x + c = 0,\]where $n$ is a positive integer, and $c$ is a real number.

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