
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
The graph of the function $$f(x)=2^{x}- \frac {a}{2^{x}}$$ is translated 2 units to the right to obtain curve C<sub>1</sub>, and the graph of the function y=g(x) is translated 2 units downward to obtain curve C<sub>2</sub>. Curve C<sub>1</sub> and C<sub>2</sub> are symmetric about the x-axis. If the minimum value of $$F(x)= \frac {f(x)}{a}+g(x)$$ is m and $$m＞2+ \sqrt {7}$$, then the range of the real number a is \_\_\_\_\_\_.

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