
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
Suppose $a, b, c$ are integers taken from the set of positive integers less than $7$ such that:
\begin{align*}
abc &\equiv 2 \pmod{7}, \\
3c &\equiv 1 \pmod{7}, \\
4b &\equiv 2 + b \pmod{7}.
\end{align*}
What is the remainder when $a+b+c$ is divided by $7$?

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