
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
The entire contents of the jug can exactly fill 9 small glasses and 4 large glasses of juice, and also fill 6 small glasses and 6 large glasses. If the entire contents of the jug is used to fill only large glasses, determine the maximum number of large glasses that can be filled.

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