
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
Determine the maximum number of real roots of the polynomial
\[ 2x^n + (2-2)x^{n-1} + (2-4)x^{n-2} + \dots + (2-2j)x^{n-j} + \dots + (2-2n)x^0 = 0, \]
where \( n \) is a positive integer and \( j \) ranges from \( 1 \) to \( n \).

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