
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
In an arithmetic progression with 12 terms, the sum of the terms is 354. The ratio of the sum of the terms with even indices to the sum of the terms with odd indices is 32:27. Determine the first term and the common difference of the progression.

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