
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 $\overrightarrow {a}=(\sqrt{3}\sin x,\sin x)$ and $\overrightarrow {b}=(\cos x,\sin x)$, where $x \in (0, \frac{\pi}{2})$,
1. If $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, find the value of $x$;
2. Let the function $f(x) = (\overrightarrow{a} + \overrightarrow{b}) \cdot \overrightarrow{b}$, determine the maximum value of $f(x)$.

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