
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
Find the number of terms in an arithmetic progression where the sum of all terms is 112, the product of the second term and the common difference is 30, and the sum of the third and fifth terms is 32. Also, write the first three terms of this progression.

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