
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
The cells of a $5 \times 7$ table are filled with numbers so that the sum of the numbers in every $2 \times 3$ rectangle (both vertical and horizontal) is zero. By paying 100 rubles, you can select any cell and find out what number is written in it. What is the minimum amount of rubles needed to definitely determine the sum of all the numbers in the table?

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