
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
The sequence {a<sub>n</sub>} is a positive and monotonically increasing geometric sequence. The sum of the first n terms is S<sub>n</sub>. $$\frac {5}{3}a_{3}$$ is the arithmetic mean of a<sub>2</sub> and a<sub>4</sub>, and S<sub>5</sub> = 484. Find the common ratio q and a<sub>3</sub>.

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