
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
Find the volume of the solid defined by the inequality  $ x^2 \plus{} y^2 \plus{} \ln (1 \plus{} z^2)\leq \ln 2$ .
Note that you may not directively use double integral here for Japanese high school students who don't study it.

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