
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)\\) is an odd function defined on \\((-1,1)\\), and when \\(x \in (0,1)\\), \\(f(x) = \dfrac{2^x}{4^x + 1}\\).

\\((1)\\) Find the expression for the function \\(f(x)\\).

\\((2)\\) Determine the monotonicity of \\(f(x)\\) on \\((0,1)\\).

\\((3)\\) For what value of \\(\lambda\\) does the equation \\(f(x) = \lambda\\) have real solutions in \\((-1,1)\\)?

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