
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
Consider an arithmetic sequence $\{a_n\}$ satisfying: the common difference $d$ is a positive integer ($d \in \mathbb{N}^*$), each term $a_n$ is a positive integer ($a_n \in \mathbb{N}^*$), and the sum of any two terms of $\{a_n\}$ is also a term in the sequence. If $a_1 = 9$, then all possible values of $d$ are ______.

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