
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 the geometric sequence {a<sub>n</sub>}, a<sub>10</sub> and a<sub>30</sub> are the two real roots of the equation x<sup>2</sup>-11x+16=0, find the value of a<sub>20</sub>.

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