
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 $$x \in [0, \frac{\pi}{2}],$$ find the range of function $f(x)$;  
(2) Find the shortest distance between two adjacent intersection points of the graph of $y=f(x)$ and the line $y=1.$

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