
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
The positive integers  $a $  and   $b $  satisfy the sistem  $\begin {cases} a_{10} +b_{10} = a a_{11}+b_{11 }=b \end {cases} $  where   $ a_1 <a_2 <\dots $  and   $ b_1 <b_2 <\dots $  are the positive divisors of  $a $  and  $b$  .
Find  $a$  and  $b $  .

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