
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
There is the sequence of numbers  $1, a_2, a_3, ...$  such that satisfies  $1 \cdot a_2  \cdot a_3 \cdot  ...  \cdot a_n = n^2$ , for every integer  $n> 2$ . Determine the value of  $a_3 + a_5$ .

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