
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
The school cafeteria serves 500 students daily, with two options, A and B, available every Monday. A survey revealed that 20% of those who chose A on a given Monday would switch to B the following Monday. Similarly, 30% of those who chose B would switch to A the next Monday. Let $a\_n (n∈N^*)$ represent the number of students choosing A on the n-th Monday. If $a\_1=428$, find the value of $a\_8$.

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