
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 that the function $f(x) = \sin^2x + \cos x + \frac{5}{8}a - \frac{3}{2}$ has a minimum value of 2 on the closed interval $\left[0, \frac{\pi}{2}\right]$, find the corresponding value of $a$.

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