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

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