
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 $f(x) = 2\sin x\cos x - 2 \sqrt {3}\cos ^2 x + \sqrt {3}$.
(1) When $x \in \left[0, \frac{\pi}{2}\right]$, find the range of the function $f(x)$;
(2) Find the shortest distance between two adjacent points of intersection of the graph of $y = f(x)$ with the line $y = 1$.

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