
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
For a geometric sequence $\{a_n\}$ with a common ratio not equal to 1, it satisfies $a_5a_6 + a_4a_7 = 18$. If $a_1a_m = 9$, determine the value of $m$.

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