
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 $f\left(x\right)= \frac{{2}^{x}}{a}+ \frac{a}{{2}^{x}}-1 \quad \left( a{ > }0 \right)$ is an even function on $\mathbb{R}$.

(1) Find the value of $a$;

(2) Solve the inequality $f(x){ < }\frac{13}{4}$;

(3) If the inequality $mf(x){\geqslant }2^{{-}x}{-}m$ holds for all $x$ in $(0,{+∞})$, find the range of possible values for the real number $m$.

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