
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
Observe the following expressions: $2^{1}=2$, $2^{2}=4$, $2^{3}=8$, $2^{4}=16$, $2^{5}=32$, $2^{6}=64\ldots $<br/>$(1)$ The unit digit of $2^{2024}$ is ______;<br/>$(2)$ The unit digit of $3^{2023}+8^{2023}$ is ______;<br/>$(3)$ If $m$ is a positive integer that cannot be divided by $4$, then the unit digit of $1^{m}+2^{m}+3^{m}+\ldots +9^{m}$ is ______.

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