
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
In the numerical sequences $\left(a_{n}\right)$ and $\left(b_{n}\right)$, each term, starting from the third, is equal to the sum of the two preceding ones, with $a_{1}=1, a_{2}=2$ and $b_{1}=2, b_{2}=1$. How many numbers appear in both the first and the second sequences?

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