
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 the vectors $\overrightarrow{a}=(\sin \theta,1)$ and $\overrightarrow{b}=(1,\cos \theta)$, where $-\dfrac{\pi}{2} < \theta < \dfrac{\pi}{2}$.
1. If $\overrightarrow{a}\perp \overrightarrow{b}$, find the value of $\tan \theta$.
2. Find the maximum value of $|\overrightarrow{a} + \overrightarrow{b}|$.

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