
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

A calculator has two special keys:

- The A key, which doubles the number displayed; and
- The B key, which adds one to the number displayed.

For example, if the number 45 is on the display and the B key is pressed, the display will show the number 46. If the A key is then pressed, the display will show the number 92. In this example, the A and B keys were pressed a total of two times: the B key once followed by the A key once, to go from 45 to 92. Suppose the number 1 is on the display. Indicate a way to obtain the number:

(a) 10 by pressing the A and B keys a total of four times;

(b) 15 by pressing the A and B keys a total of six times;

(c) 100 by pressing the A and B keys a total of eight times.

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