
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 an arithmetic sequence $\{a_n\}$ with a common difference $d \neq 0$, and $a_1$, $a_3$, $a_9$ form the first $3$ terms of a geometric sequence $\{b_n\}$, then $\dfrac{a_1+a_3+a_6}{a_2+a_4+a_10}=$ ______.

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