
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 function defined on \\(R\\), \\(f(x) = 2^{x} - \frac{1}{2^{|x|}}\\).
\\((1)\\) If \\(f(x) = \frac{3}{2}\\), find the value of \\(x\\);
\\((2)\\) If \\(2^{t}f(2t) + mf(t) \geqslant 0\\) holds for all \\(t \in [1,2]\\), find the range of the real number \\(m\\).

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