
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]


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If $a, b, c, d$ are non-negative integers less than $11$ such that
\begin{align*}
a + 3b + 4c + 2d &\equiv 3 \pmod{11}, \\
3a + b + 2c + d &\equiv 5 \pmod{11}, \\
2a + 4b + c + 3d &\equiv 7 \pmod{11}, \\
a + b + c + d &\equiv 2 \pmod{11},
\end{align*}
determine the remainder when $abcd$ is divided by $11$.

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