
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 11 cents worth of postage in a row across the top of an envelope? Similar restrictions apply regarding the rotation or inverting of stamps, or exchanging positions of stamps with the same denomination.

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