
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

Joseane's calculator is malfunctioning: each digit pressed appears doubled on the screen. The addition, subtraction, multiplication, and division operation keys work normally and cannot be pressed consecutively twice. For example, a permissible sequence of operations is pressing $2 \rightarrow \times \rightarrow 3$, which produces the number $4 \cdot 6=24$.

a) How can she make 80 appear by pressing 3 keys?

b) How can she make 50 appear by pressing 3 number keys and two operation keys alternately?

c) What is the minimum number of keys she must press to obtain the number 23?

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