
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 $\overset{→}{a}=(\sin θ,1), \overset{→}{b}=(1,\cos θ)$, where $-\dfrac{\pi }{2} < θ < \dfrac{\pi }{2}$.

(1) Find $θ$ if $\overset{→}{a} \bot \overset{→}{b}$;

(2) Find the maximum value of $|\overset{→}{a}+\overset{→}{b}|$.

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