
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
Call a positive integer one-full if it satisfies the following criteria:

(a) Every digit is either 0, 1, or 2.

(b) Out of every two consecutive digits, at least one of them is a 1.

For \( n \geq 2 \), calculate the number of \( n \)-digit one-full numbers. (Numbers beginning with the digit 0 are not allowed.)

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