
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 $\overrightarrow{a} = (\sqrt{3}\sin{\omega x}, \cos{\omega x})$ and $\overrightarrow{b} = (\cos{\omega x}, \cos{\omega x})$, where $\omega > 0$, define the function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$. If $f(x)$ has the smallest positive period as $\pi$:
(Ⅰ) Find $\omega$;
(Ⅱ) When $0 < x \leq \frac{\pi}{3}$, find the range of $f(x)$.

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