
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 initially writes the number 4 on his thumb. He then applies function $f$ to 4 and writes the output on his next finger. Larry repeats this process, applying $f$ and writing the output on a new finger each time. If the new function $f$ maps numbers as follows seen in a graph: \(f(4) = 7\), \(f(7) = 8\), \(f(8) = 3\), \(f(3) = 5\), \(f(5) = 4\) (forming a cycle every five applications), what number will Larry write on his twelfth finger?

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