
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 \\(a \in \mathbb{R}\\), the function \\(f(x) = \log_2\left(\frac{1}{x} + a\right)\\)

\\((1)\\) When \\(a=1\\), solve the inequality \\(f(x) > 1\\);

\\((2)\\) If the solution set of the equation \\(f(x) + \log_2(x^2) = 0\\) regarding \\(x\\) contains exactly one element, find the value of \\(a\\);

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