
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 $$\overrightarrow {m}=(a^{x},-a), \overrightarrow {n}=(a^{x},a)$$, where $a>0$ and $a\neq 1$,  
(1) For what value of $x$ is $$\overrightarrow {m}\perp \overrightarrow {n}$$;  
(2) Solve the inequality about $x$: $$| \overrightarrow {m}+ \overrightarrow {n}|<| \overrightarrow {m}- \overrightarrow {n}|$$.

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