
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

If $2008=2^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{n}}$, where $a_{1}, a_{2}, \cdots, a_{n}$ are distinct non-negative integers, then the relationship between $\sin \sum_{i=1}^{n} a_{i}$, $\cos \sum_{i=1}^{n} a_{i}$, and $\tan \sum_{i=1}^{n} a_{i}$ is ______. (Given that $\pi=3.141592 \cdots$)

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