
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 host is waiting for 7 or 11 children and has prepared 77 marbles as gifts. He wants to distribute these marbles into \(n\) bags so that each child (whether 7 or 11) can receive several bags of marbles, and the 77 marbles must be equally divided among the children. Find the minimum value of \(n\).

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