
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 $f(x) = e^x$, its graph at point $P(2, f(2))$ has a tangent line $l$.  
(1) Find the volume of the solid formed by rotating the region bounded by $y=f(x)$, the line $x=2$, and the two coordinate axes around the x-axis.  
(2) Find the area of the region bounded by $y=f(x)$, the line $l$, and the y-axis.

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