
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
For each real number x, define the polynomial P(x) = 2 + e^(ix) - 2e^(2ix) + e^(3ix), where i = √(-1). Determine the number of distinct values of x that satisfy P(x) = 0 for 0 ≤ x < 2π.

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