
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 vectors $\overrightarrow{a} = (1, \cos(\omega x - \frac{\pi}{6}))$ and $\overrightarrow{b} = (\sqrt{3}, \sqrt{3} \sin(\omega x - \frac{\pi}{6}))$, where $\omega$ is a constant and $\omega > 0$.
(1) If $\omega = 1$ and $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, find the value of $\tan x$.
(2) Define the function $f(x) = (\overrightarrow{a} - \overrightarrow{b})^2 - (\sqrt{3} - 1)^2$. If the smallest positive period of $f(x)$ is $\pi$, find the range of $f(x)$ when $x \in (0, \frac{\pi}{2})$.

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