
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 $\overset{→}{m}=( \frac{ \sqrt{2}}{2},- \frac{ \sqrt{2}}{2})$ and $\overset{→}{n}=(\sin x,\cos x)$, where $x \in (0, \frac{π}{2})$.

(1) If $\overset{→}{m} \perp \overset{→}{n}$, find the value of $\tan x$;

(2) If the angle between $\overset{→}{m}$ and $\overset{→}{n}$ is $\frac{π}{3}$, find the value of $x$.

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