
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
Consider a stripe of  $n$  fieds, numbered from left to right with the integers  $1$  to  $n$  in ascending order. Each of the fields is colored with one of the colors  $1$ ,  $2$  or  $3$ . Even-numbered fields can be colored with any color. Odd-numbered fields are only allowed to be colored with the odd colors  $1$  and  $3$ .
How many such colorings are there such that any two neighboring fields have different colors?

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