
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 two vectors, $\overrightarrow{a} = (\sqrt{3}\cos x - \sqrt{3}, \sin x)$ and $\overrightarrow{b} = (1 + \cos x, \cos x)$, let $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$.
(1) Find the value of $f\left(\frac{25\pi}{6}\right)$.
(2) When $x \in \left[-\frac{\pi}{3}, \frac{\pi}{6}\right]$, find the range of the function $f(x)$.

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