
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
Let  $a_1=1$  and  $a_{n+1}=2/(2+a_n)$  for all  $n\geqslant 1$ . Similarly,  $b_1=1$  and  $b_{n+1}=3/(3+b_n)$  for all  $n\geqslant 1$ . Which is greater between  $a_{2022}$  and  $b_{2022}$ ?

*Proposed by P. Kozhevnikov*

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