
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 $$f(x)= \frac {2^{x}}{a}+ \frac {a}{2^{x}}-1   (a＞0)$$ is an even function over $\mathbb{R}$.  
(1) Find the value of $a$;  
(2) Solve the inequality $$f(x)＜ \frac {13}{4}$$;  
(3) If the inequality $mf(x) \geq 2^{-x} - m$ holds true over $(0, +\infty)$ for $x$, find the range of the real number $m$.

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