
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
Let \(a, b, c\) be non-negative integers less than \(7\) such that
\[
a + 3b + 2c \equiv 2 \pmod{7},
2a + b + 3c \equiv 3 \pmod{7},
3a + 2b + c \equiv 5 \pmod{7}.
\]
Determine the remainder when \(abc\) is divided by \(7\).

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