
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
Integers \(0 \leq a, b, c, d \leq 9\) satisfy the following system of equations:
\[
\begin{array}{c}
6a + 9b + 3c + d = 88 \\
a - b + c - d = -6 \\
a - 9b + 3c - d = -46
\end{array}
\]
Find \(1000a + 100b + 10c + d\).

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