
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 remainders when four positive integers are divided by 7 are 2, 3, 5, and 6. Find the remainder when the sum of the product of the first two integers and the product of the last two integers is divided by 7.

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