
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
Two cones are constructed on the bases of a cylinder with a square axial cross-section, such that the vertices of the cones lie at the midpoint of the cylinder's axis. Find the sum of the total surface areas and the sum of the volumes of the cones if the height of the cylinder is $2a$.

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