
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
Suppose an arithmetic sequence \{a_n\} has the sum of its first n terms denoted by A_n, and a geometric sequence \{b_n\} has the sum of its first n terms denoted by B_n. If a_3 = b_3, a_4 = b_4, and $$\frac {A_{5}-A_{3}}{B_{4}-B_{2}}=7$$, then find the common ratio q of the geometric sequence \{b_n\}.

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