
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 \( 5 \) such that:
\[
abc \equiv 1 \pmod{5},
\]
\[
4c \equiv 3 \pmod{5},
\]
\[
3b \equiv 2 + b \pmod{5},
\]
then what is the remainder when \( a+b+c \) is divided by \( 5 \)?

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