
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
Compute the following triple integrals:

1) \( I = \iiint_{G} \frac{dx\, dy\, dz}{(x+y+z+1)^{3}} \), where the region \( G \) is bounded by the planes \( x+z=3 \), \( y=2 \), \( x=0 \), \( y=0 \), \( z=0 \);

2) \( J = \iiint_{W} \left(x^{2}+y^{2}+z^{2}\right) dx\, dy\, dz \), where the region \( W \) is bounded by the surface \( 3\left(x^{2}+y^{2}\right)+z^{2}=3a^{2} \);

3) \( K = \iiint_{T} y\, dx\, dy\, dz \), where the region \( T \) is bounded by the surfaces \( y=\sqrt{x^{2}+z^{2}} \) and \( y=h \), \( h>0 \).

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