
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 \\(f(x) = (x + m)^{2n + 1}\\) and \\(g(x) = (mx + 1)^{2n}\\) where \\(n \in \mathbb{N}^+\) and \\(m \neq 0\).

\\((1)\\) If \\(n = 3\\), the coefficient of the \\(x^3\\) term in the expansions of \\(f(x)\\) and \\(g(x)\\) are equal, find the value of the real number \\(m\\).

\\((2)\\) If the coefficient of the \\(x^n\\) term in the expansions of \\(f(x)\\) and \\(g(x)\\) are equal, find the range of values for the real number \\(m\\).

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