
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 frame for a rectangular container is made from a 6m long steel bar. If the ratio of the adjacent side lengths of the base of the container is 3:4, find the height of the container when its volume is maximized.

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