
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 $$\overrightarrow {m}=( \sqrt {3}\sin x+\cos x,1), \overrightarrow {n}=(\cos x,-f(x)), \overrightarrow {m}\perp \overrightarrow {n}$$.
(1) Find the monotonic intervals of $f(x)$;
(2) Given that $A$ is an internal angle of $\triangle ABC$, and $$f\left( \frac {A}{2}\right)= \frac {1}{2}+ \frac { \sqrt {3}}{2},a=1,b= \sqrt {2}$$, find the area of $\triangle ABC$.

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