
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
There is a set of 6860 switches, each with five positions named $A, B, C, D, E$. The positions change cyclically from $A$ to $B$, $B$ to $C$, $C$ to $D$, $D$ to $E$, and $E$ back to $A$. Each switch is initially in position $A$. The switches are labeled with numbers of the form $(2^{x})(3^{y})(5^{z})(7^{w})$ where $x, y, z, w$ take on values $0, 1, \ldots, 5$. For step $i$ of a 6860-step process, the $i$-th switch is advanced one step, along with all other switches whose labels divide the label on the $i$-th switch. After all steps are completed, how many switches will be in position $A$?

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