
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
A block  $Z$  is formed by gluing one face of a solid cube with side length 6 onto one of the circular faces of a right circular cylinder with radius  $10$  and height  $3$  so that the centers of the square and circle coincide. If  $V$  is the smallest convex region that contains Z, calculate  $\lfloor\operatorname{vol}V\rfloor$  (the greatest integer less than or equal to the volume of  $V$ ).

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