
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 $\overrightarrow{OP} = (2\cos x + 1, \cos 2x - \sin x + 1)$ and $\overrightarrow{OQ} = (\cos x, -1)$, define $f(x) = \overrightarrow{OP} \cdot \overrightarrow{OQ}$.
(1) Find the smallest positive period of the function $f(x)$;
(2) If $x \in (0, 2\pi)$, find the range of $x$ when $\overrightarrow{OP} \cdot \overrightarrow{OQ} < -1$.

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