
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
What is the smallest positive integer that, when divided by:
- 6 leaves a remainder of 5,
- 7 leaves a remainder of 6,
- 8 leaves a remainder of 7,
- 9 leaves a remainder of 8,
- 10 leaves a remainder of 9,
- 11 leaves a remainder of 10,
- 13 leaves a remainder of 12?

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