
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 the function $f(x) = \sin \omega x \cdot \cos \omega x - \cos^2 \omega x$ ($\omega > 0$), its smallest positive period is:

(Ⅰ) Find the value of $\omega$;

(Ⅱ) Suppose $\triangle ABC$ has sides $a$, $b$, $c$ satisfying $b^2 = ac$, and the angle opposite to side $b$ is $x$, find the range of $f(x)$ under this condition.

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