
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
Let \\(f(x) = x^{2} - (t + 1)x + t \quad (t, x \in \mathbb{R})\\).
\\((1)\\) When \\(t = 3\\), find the solution set of the inequality \\(f(x) > 0\\).
\\((2)\\) Given that \\(f(x) \geqslant 0\\) holds for all real numbers \\(x\\), find the value of \\(t\\).

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