
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
On a $5 \times 7$ grid, 9 cells are marked. We define a pair of cells sharing a side as interesting if at least one cell in the pair is marked. What is the maximum number of interesting pairs that can be formed?

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