
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
Given the following system of equations, find the product \(a \cdot b \cdot c \cdot d\):
\[
\begin{align*}
4a - 2b + 3c + 5d &= 22, \\
2(d+c) &= b - 2, \\
4b - c &= a + 1, \\
c + 1 &= 2d.
\end{align*}
\]

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