
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 vectors $\overrightarrow{a}=(\cos \frac{3x}{2},\sin \frac{3x}{2})$, $\overrightarrow{b}=(\cos \frac{x}{2},-\sin \frac{x}{2})$, and $|\overrightarrow{a}+ \overrightarrow{b}|=1, x\in[0,\pi]$, find $x$.

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