
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 Mystic Four Calculator has a four-digit display and four buttons. The calculator works as follows: 
- Pressing button 1 replaces the number in the display with 1.
- Pressing button 2 divides the number in the display by 2.
- Pressing button 3 subtracts 3 from the number in the display.
- Pressing button 4 multiplies the number in the display by 4.

Initially, the display shows 0. Any operation yielding a negative, fractional, or five-digit answer is ignored.

(a) Can 2007 appear in the display?

(b) Can 2008 appear in the display?

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