
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 $\overrightarrow{m} = (\sin(x - \frac{\pi}{3}), 1)$ and $\overrightarrow{n} = (\cos x, 1)$.

(1) If $\overrightarrow{m} \parallel \overrightarrow{n}$, find the value of $\tan x$.

(2) If $f(x) = \overrightarrow{m} \cdot \overrightarrow{n}$, where $x \in [0, \frac{\pi}{2}]$, find the maximum and minimum values of $f(x)$.

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