
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
Diane has one 1-cent stamp, two identical 2-cent stamps, and so on, up to ten identical 10-cent stamps. Determine how many different arrangements can Diane paste exactly 15 cents worth of postage in a row across the top of an envelope, where rotations or inversions of stamps, or exchanging positions of two stamps with the same denomination are considered the same arrangement.

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