
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
Suppose the function $g$ is graphed, and each small box on the graph has width and height 1. The function values at specific $x$ coordinates are provided as follows: $g(0)=0$, $g(2)=1$, $g(4)=3$, $g(6)=5$, $g(8)=7$, $g(1)=8$, $g(3)=6$, $g(5)=4$, $g(7)=2$, $g(9)=0$. Sara writes the number 4 on her thumb and applies $g$ to 4, writing the output on her next finger. She continues this process of applying $g$ and writing the output on the next finger. What number will Sara write on her tenth finger?

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