
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
Manzi has  $n$  stamps and an album with  $10$  pages. He distributes the  $n$  stamps in the album such that each page has a distinct number of stamps. He finds that, no matter how he does this, there is always a set of  $4$  pages such that the total number of stamps in these  $4$  pages is at least  $\frac{n}{2}$ . Determine the maximum possible value of  $n$ .

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