
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 the function $f(x) = \cos x(\sin x + \sqrt{3}\cos x) - \frac{\sqrt{3}}{2}, x \in \mathbb{R}$, let $a > 0$. If the function $g(x) = f(x + \alpha)$ is an odd function, then the value of $\alpha$ is ______.

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