
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 integer $n$ greater than 1, let $G(n)$ be the number of solutions of the equation $\cos x = \cos nx$ on the interval $[0, \pi]$. What is $\sum_{n=2}^{2007} G(n)$?

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