
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
(In this question, full marks are 15 points) Given a rectangular piece of paper ABCD, where AB = 6 cm and AD = 12 cm. The bottom right corner of the rectangle is folded up so that the vertex B falls on the edge AD of the rectangle, and the fold line MN has its endpoints M and N on the edges AB and BC, respectively. Let $\angle MNB = \theta$, $\sin\theta = t$, and the length of MN is $l$.
(1) Express $l$ as a function of $t$, $l = f(t)$;
(2) Find the minimum value of $l$.

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