
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 $f\left( x \right)=ax\sin x-\frac{3}{2}\left( a\in R \right)$, and its maximum value on $\left[ 0,\frac{\pi }{2} \right]$ is $\frac{\pi -3}{2}$, find the value of the real number $a$.

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