
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
In each cell of a \(5 \times 5\) table, an invisible integer is written. It is known that the sum of all the numbers is 200, and the sum of three numbers in any \(1 \times 3\) rectangle is 23. What is the value of the central number in the table?

![Table](https://cdn.mathpix.com/cropped/2024_05_06_c49ecf27446af41a8bcdg-39.jpg?height=309&width=311&top_left_y=340&top_left_x=575)

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