
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 $\overrightarrow{a} = (\sin x, \frac{3}{2})$ and $\overrightarrow{b} = (\cos x, -1)$,
(1) Find the value of $\tan x$ when $\overrightarrow{a} \parallel \overrightarrow{b}$;
(2) Find the maximum value of $f(x) = \overrightarrow{a} \cdot \overrightarrow{b} + \overrightarrow{b}^{2}$ and determine the set of values of $x$ for which $f(x)$ reaches its maximum.

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