
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
The function $g$ is graphed below. Each small box has width and height 1. 

Larry writes the number 4 on his thumb. He then applies $g$ to 4 and writes the output on his index finger. If Larry continues this process of applying $g$ and writing the output on a new finger, what number will Larry write on his eighth finger?

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