
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 that the function $f(x)=\log_{3}(a+x)+\log_{3}(2-x)\ (a∈R)$ is an even function.
(1) If $f(p)=1$, find the value of the real number $p$;
(2) If there exists an $m$ such that $f(2m-1) < f(m)$ holds, find the range of values for the real number $m$.

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