
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 $f(x) = x^2 - (t+1)x + t$ ($t, x \in \mathbb{R}$).

(1) When $t=3$, find the solution set of the inequality $f(x) > 0$.

(2) Given that $f(x) \geq 0$ holds for all real numbers $x$, find the value of $t$.

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