
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 \\(f(x)\\) and \\(g(x)\\) are both differentiable functions defined on \\(\mathbb{R}\\), and satisfy the following conditions:  
\\(① g(x) \neq 0\\)  
\\(② f(x) = 2a^{x}g(x) (a > 0, a \neq 1)\\)  
\\(③ f(x)g′(x) < f′(x)g(x)\\)  
If \\( \dfrac {f(1)}{g(1)} + \dfrac {f(-1)}{g(-1)} = 5\\), then \\(a=\\) ______.

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