
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
In a monotonically increasing geometric sequence $\{a_n\}$, $a_1 \cdot a_9 = 64$, $a_3 + a_7 = 20$, find $a_{11} =$ ______.

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