
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
Suppose that $a$ and $b$ are integers such that $$4b = 10 - 3a.$$ How many of the first eight positive integers must be divisors of $3b + 15$?

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