
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
When the ninth term of an arithmetic sequence is divided by the second term, the quotient is 5. When the thirteenth term is divided by the sixth term, the quotient is 2 with a remainder of 5. Find the first term and the common difference of the sequence.

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