
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 $\overrightarrow {m}$=($\frac { \sqrt {2}}{2}$,$- \frac { \sqrt {2}}{2}$) and $\overrightarrow {n}$=(sinx,cosx), where x∈(0,$\frac {π}{2}$).
(1) If $\overrightarrow {m}$ is perpendicular to $\overrightarrow {n}$, find the value of tanx.
(2) If the angle between vectors $\overrightarrow {m}$ and $\overrightarrow {n}$ is $\frac {π}{3}$, find the value of cos2x.

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