
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
Let \( a \), \( b \), \( c \), and \( d \) be real numbers satisfying:
\begin{align*}
a + b + c &= 5, \\
a + b + d &= -1, \\
a + c + d &= 8, \text{ and} \\
b + c + d &= 12.
\end{align*}
Calculate \( ab + cd \).

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