
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
Consider the curve \( y = \mathrm{e}^{-x} \) (for \( x \geq 0 \)). At point \( M(t, \mathrm{e}^{-t}) \), let the tangent line \( l \) form a triangle with the \( x \)-axis and the \( y \)-axis. Let the area of this triangle be \( S(t) \).

1. Find the equation of the tangent line \( l \).
2. Find the maximum value of \( S(t) \).

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