
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 product of the third and sixth terms of an arithmetic sequence is 406. When the ninth term of this sequence is divided by the fourth term, the quotient is 2 and the remainder is 6. Find the first term and the common difference of the sequence.

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