
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 $\overrightarrow{a}=(\sin\theta, \sqrt{3})$ and $\overrightarrow{b}=(1, \cos\theta)$, where $\theta \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.
(1) If $\overrightarrow{a} \perp \overrightarrow{b}$, find $\theta$;
(2) Find the maximum value of $|\overrightarrow{a} + \overrightarrow{b}|$.

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