
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
Let \(\left(\frac{\sqrt{3}}{2}+\frac{x}{2} \mathrm{i}\right)^{2008}=f(x)+\mathrm{i} g(x)\), where \(f(x)\) and \(g(x)\) are polynomials with real coefficients. Find the sum of the coefficients of \(f(x)\).

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