
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 $$\overrightarrow {a}=(\sin\theta，1)， \overrightarrow {b}=(1，\cos\theta)$$,  
(1) If $$\overrightarrow {a} \perp \overrightarrow {b}$$ and $$- \frac {\pi}{2}＜\theta＜ \frac {\pi}{2}$$, find $\theta$;  
(2) Find the interval of monotonic increase for the function $$y=| \overrightarrow {a}+ \overrightarrow {b}|$$ and the equation of the axis of symmetry for the graph of the function.

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