
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 $t > 0$, it is known that the graph of the function $f(x) = x^2(x - t)$ intersects the x-axis at points A and B.  
(1) Determine the intervals of monotonicity for the function $f(x)$.  
(2) Suppose the slope of the tangent line to the graph of $y = f(x)$ at point $P(x_0, y_0)$ is $k$, and when $x_0 \in (0, 1]$ it holds that $k \geq -1$ always, find the maximum value of $t$.  
(3) There is a line $l$ parallel to the x-axis that intersects the graph of $y = f(x)$ at two distinct points C and D. If the quadrilateral ABCD is a rhombus, find the value of $t$.

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