
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  $a$  and  $b$  be positive whole numbers such that  $\frac{4.5}{11}<\frac{a}{b}<\frac{5}{11}$ . 
Find the fraction  $\frac{a}{b}$  for which the sum  $a+b$  is as small as possible. 
Justify your answer

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