
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 are 10 students standing in a row. A teacher wants to assign a hat to each student, with the hats available in two colors: red and white. There are more than 10 hats of each color available. The requirement is that in any consecutive group of students, the difference between the number of students wearing red hats and the number of students wearing white hats is at most 2. How many ways can the teacher assign the hats?

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