
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 $\overrightarrow{a}=(\cos \frac {3x}{2},\sin \frac {3x}{2}), \overrightarrow{b}=(\cos \frac {x}{2},\sin \frac {x}{2})$:

1. Find $x$ if $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$ and $x \in [0, \frac{\pi}{2}]$.
2. If $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$, write the interval where $f(x)$ is monotonically decreasing.

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