
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 the ellipse \\(C: \dfrac{x^2}{m^2} + y^2 = 1\\) with its left and right foci being \\(F_1\\) and \\(F_2\\), respectively, and its eccentricity is \\(\dfrac{\sqrt{2}}{2}\\).

\\((1)\\) Find the equation of the ellipse \\(C\\);

\\((2)\\) Let the line \\(l: y = x + t \begin{matrix} {} & (t > 0) \end{matrix}\\) intersect the ellipse \\(C\\) at points \\(A\\) and \\(B\\). If the origin \\(O\\) is inside the circle with diameter \\(AB\\), find the range of the real number \\(t\\).

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