
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 \( f(x)=\sqrt{3} \sin 2x + 2 \cos^2 x + a \), if the minimum value of \( f(x) \) on the interval \(\left[ 0, \frac{\pi}{2} \right] \) is \(-1\), find the value of \( a \).

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