
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 eight identical 8-cent stamps. In how many different arrangements can Diane paste exactly 12 cents worth of postage in a row across the top of an envelope? Rotating or inverting a stamp, or exchanging the positions of two stamps with the same denomination should be considered the same arrangement.

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