
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 a line $l$ passing through point $P(-1, 2)$, and the cosine of its inclination angle is $\frac{\sqrt{2}}{2}$.

(1) Find the general form equation of line $l$;  
(2) Calculate the volume of the geometric body formed by rotating the triangle enclosed by line $l$ and the coordinate axes around the y-axis in space.

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