
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 $f(x)=\log_{3}(m^{x}+1)-x(m>0$, and $m\neq 1)$ is an even function.<br/>$(1)$ Find the value of $m$;<br/>$(2)$ If the inequality in terms of $x$, $\frac{1}{2}\cdot 3^{f(x)}-3[(\sqrt{3})^{x}+(\sqrt{3})^{-x}]+a\leq 0$ has a solution on $R$, find the maximum integer value of the real number $a$.

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