
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
Every member, starting from the third one, of two sequences  $\{a_n\}$  and  $\{b_n\}$  equals to the sum of two preceding ones. First members are:  $a_1 = 1, a_2 = 2, b_1 = 2, b_2 = 1$ . How many natural numbers are encountered in both sequences (may be on the different places)?

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