
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
There is a math game on a computer: each time the $A$ key is pressed, the number on the screen increases by $3$; each time the $B$ key is pressed, the number on the screen is multiplied by $(-2)$; each time the $C$ key is pressed, the number on the screen is divided by $4$. It is known that the initial number on the screen is $-1$. For example, if the key sequence is $A \rightarrow B$, then the number displayed on the screen is $-4$.

$(1)$ If the number displayed on the screen is maximized after pressing two keys in a row (without repeating $A$, $B$, or $C keys), then the key sequence is ______;

$(2)$ If the key sequence is $A \rightarrow B \rightarrow C \rightarrow A \rightarrow B \rightarrow C \ldots $, following this key pattern, after pressing $2023$ times, the number displayed on the screen is ______.

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