
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
In the Cartesian coordinate system xOy, given vectors $$\overrightarrow {m} = \left( \frac { \sqrt {2}}{2}, -\frac { \sqrt {2}}{2} \right)$$ and $$\overrightarrow {n} = (\sin x, \cos x)$$, where \(x \in (0, \frac {\pi}{2})\).
1. If $$\overrightarrow {m} \perp \overrightarrow {n}$$, find the value of \(\tan x\);
2. If the angle between $$\overrightarrow {m}$$ and $$\overrightarrow {n}$$ is $$\frac {\pi}{3}$$, find the value of \(x\).

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