
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 a geometric sequence {a_n}, where a_3a_{11}=4a_7, and a sequence {b_n} is an arithmetic sequence with b_7=a_7, calculate the value of b_5+b_9.

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