
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
Given an infinitely decreasing geometric series. The sum of all its terms with odd indices is 2 more than the sum of all its terms with even indices. The difference between the sum of the squares of all terms at odd positions and the sum of the squares of all terms at even positions is $\frac{36}{5}$. Find the first term and the common ratio of the series.

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