
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 $\left(\cos \theta +i\sin \theta \right)^{n}=\cos n\theta +i\sin n\theta$ (where $i$ is the imaginary unit, $n\in \mathbb{N}^{*}$, and $\theta \in \mathbb{R}$), if a complex number $z$ satisfies $z\cdot\left(\cos\frac{\pi}{9}+\ i\sin\frac{\pi}{9}\right)^{6}=2$, calculate $|z|$.

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