
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 the function $f(x)=2^{x}$ with its inverse function $f^{-1}(x)$,
(1) If $f^{-1}(x)-f^{-1}(1-x)=1$, find the value of the real number $x$;
(2) If the equation $f(x)+f(1-x)-m=0$ has solutions in the interval $[0,2]$, find the range of values for the real number $m$.

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