
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
Arrange 25 numbers into a 5 by 5 matrix:

\begin{matrix}
a_{11} & a_{12} & a_{13} & a_{14} & a_{15} \\
a_{21} & a_{22} & a_{23} & a_{24} & a_{25} \\
a_{31} & a_{32} & a_{33} & a_{34} & a_{35} \\
a_{41} & a_{42} & a_{43} & a_{44} & a_{45} \\
a_{51} & a_{52} & a_{53} & a_{54} & a_{55} \\
\end{matrix}

The first row forms an arithmetic sequence, and each column forms a geometric sequence with the same common ratio for all columns. If $a_{24}=4$, $a_{41}=-2$, $a_{43}=10$, find the value of $a_{11} \cdot a_{55}$.

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