
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
There are many  $a\times b$  rectangular cardboard pieces ( $a,b\in\mathbb{N}$  such that  $a<b$ ). It is given that by putting such pieces together without overlapping one can make  $49\times 51$  rectangle, and  $99\times 101$  rectangle. Can one uniquely determine  $a,b$  from this?

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