
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
There is an inverted conical container with a base that is a horizontal equilateral triangle with side length 6. The container is filled with water. Now, a rectangular prism with base side length \( a \) (where \( a < 6 \)) and height \( h \) (where \( h > 6 \)) is submerged vertically in the container. To maximize the amount of water that overflows from the container, the value of \( a \) should be \(\quad\).

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