
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 three-digit positive integer \( n \) has digits \( a, b, c \). (That is, \( a \) is the hundreds digit of \( n \), \( b \) is the tens digit of \( n \), and \( c \) is the ones (units) digit of \( n \).) Determine the largest possible value of \( n \) for which:
- \( a \) is divisible by 2,
- the two-digit integer \( ab \) (where \( a \) is the tens digit and \( b \) is the ones digit) is divisible by 3 but is not divisible by 6, and
- \( n \) is divisible by 5 but is not divisible by 7.

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