
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 parabola \\(C: y^2 = 2px (p > 0)\\) with focus \\(F\\), a line with slope \\(\sqrt{2}\\) intersects the parabola at points \\(A(x_1, y_1), B(x_2, y_2) (x_1 < x_2)\\), and \\(|AB| = 6\\).

\\((1)\\) Find the equation of parabola \\(C\\).

\\((2)\\) Given a point \\(M(t, 4)\\) on the parabola, chords \\(MD\\) and \\(ME\\) are drawn from \\(M\\) such that \\(MD \perp ME\\). Determine whether the line \\(DE\\) passes through a fixed point, and explain the reason.

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