
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 how many values of the digit $A$ is it true that $45$ is divisible by $A$, and $357{,}1A6$ is divisible by $4$ and $5$?

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