
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 plane rectangular coordinate system $(xoy)$, given vectors $\overset{→}{m}=(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2})$ and $\overset{→}{n}=(\sin x,\cos x)$, where $x\in (0,\frac{\pi }{2})$:
1. If $\overset{→}{m}\perp \overset{→}{n}$, find the value of $\tan x$;
2. If the angle between $\overset{→}{m}$ and $\overset{→}{n}$ is $\frac{\pi }{3}$, find the value of $x$.

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