
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
Stephen's calculator displays only one digit. Each time he switches it on, each of the seven bars will either illuminate or not, with a probability of 0.5. The resultant display correctly shows one of the ten digits 0 - 9 with a probability \(\frac{a}{b}\). Given that \(\frac{a}{b}\) is in its lowest terms, what is the value of \(9a + 2b\)?

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