
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
Let the arithmetic sequence $\{a_n\}$ satisfy: the common difference $d\in \mathbb{N}^*$, $a_n\in \mathbb{N}^*$, and any two terms' sum in $\{a_n\}$ is also a term in the sequence. If $a_1=3^5$, then the sum of all possible values of $d$ is .

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