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

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