
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
Given the function $g$ defined by the points:
\[ g(1)=8, g(2)=7, g(3)=6, g(4)=5, g(5)=4, g(6)=3, g(7)=2, g(8)=1, g(9)=0 \]
Alex writes the number 2 on his thumb. He then applies $g$ to 2 and writes the resulting output on his index finger. If Alex continues this process of applying $g$ to the previously written number and writing the output on a new finger, what number will Alex write on his twelfth finger?

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