
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 transparent, sealed cubic container is exactly half filled with water. When this cube is rotated arbitrarily, the shape of the water surface inside the container can be: (1) triangle; (2) rectangle; (3) square; (4) regular hexagon. Among these, the correct conclusions are __________.

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