
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
Given a complex number \( z \), define the sequence \( z_0, z_1, z_2, \ldots \) such that \( z_0 = z \) and \( z_{n+1} = 2z_n^2 + 2z_n \) for \( n \geq 0 \). Given that \( z_{10} = 2017 \), find the minimum possible value of \( |z| \).

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