
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
(The full score for this sub-question is 13 points.)
It is known that the function $f(x) = \sin(\omega x) \cdot \cos(\omega x) - \cos^2(\omega x)$ ($\omega > 0$) has the minimum positive period of $T$.

(Ⅰ) Find the value of $\omega$;

(Ⅱ) Suppose the sides $a$, $b$, and $c$ of triangle $ABC$ satisfy $b^2 = ac$, and the angle opposite to side $b$ is $x$, find the range of $f(x)$ in this case.

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