
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 function $f(x) = -3x^2 + 6x$, and the lines $l_1: x = t$, $l_2: x = t + 1$ (where $0 \leq t \leq 2$, $t$ is a constant), if the enclosed area formed by the lines $l_1$, $l_2$, the x-axis, and the curve $y = f(x)$ is denoted as $S(t)$.

(1) Find the expression for $S(t)$;  
(2) As $t$ varies, find the maximum value of $S(t)$.

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