
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
Pepi needs to place all the numbers from 1 to 8 on the following board so that the sum of the two numbers placed in each column is always the same value $S$.

|  |  |  |  |
| :--- | :--- | :--- | :--- |
|  |  |  |  |

a) Show Pepi a way to place the numbers.

b) Convince Pepi that the only possible value for $S$ is 9.

c) Calculate the number of ways Pepi can place the numbers.

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