
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
\begin{align*}
3a + 2b + 4c + 6d &= 60 \\
4(d+c) &= b^2 \\
4b + 2c &= a \\
c - 2 &= d \\
\end{align*}
Given this system of equations, find $a \cdot b \cdot c \cdot d$.

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