
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 definition: the multiplication of $n$ times $a$ is represented as $\underbrace{\mathrm{a} \times \mathrm{a} \times \cdots \times \mathrm{a} \times \bar{c}}_{\mathrm{n} \text { of }a }=a^{n}$. Observe the following calculations: $8^{1}=8$, $8^{2}=64$, $8^{3}=512$, $8^{4}=4096$, $8^{5}=32768$, $8^{6}=262144$, $8^{7}=2097152$, $8^{8}=16777216$, etc. Find the remainder when $8^{2012}$ is divided by 10.

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