
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
In the Cartesian coordinate system, given points A(2,0), B(0,2), and C(cos2x, sin2x), let $f(x) = \overrightarrow{AB} \cdot \overrightarrow{AC}$.
(1) Determine the expression for $f(x)$ and its minimum positive period;
(2) When $0 < x < \frac{\pi}{2}$, find the range of $f(x)$.

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