
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
Larry now starts with the number 4 on his pinky finger. He applies function $f$ to 4 and writes the output on his ring finger. Then, instead of applying $f$ again, he uses a new function $g$ defined on the same set of points. If Larry alternates between applying $f$ and $g$, what number will Larry write on his tenth finger? The functions $f$ and $g$ at different points are defined as follows based on the previous graph data:
- $f(4) = 3$
- $g(3) = 1$
- $f(1) = 8$
- $g(8) = 7$
- $f(7) = 2$
- $g(2) = 1$
- $f(1) = 8$ (repetition starts here)

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