
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 graph of the function $f(x)=2a\sin^2x+2\sin x\cos x-a$ passes through the point $(0, -\sqrt{3})$.  
(1) Determine the constant $a$;  
(2) When $x \in [0, \frac{\pi}{2}]$, find the range of the function $f(x)$.

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