
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
If $n \in \mathbb{N}^*$, and $n$ is an odd number, then the remainder obtained when dividing $6^{n}+C_{n}^{1} \cdot 6^{n-1}+C_{n}^{2} \cdot 6^{n-2}+...+C_{n}^{n-1} \cdot 6$ by $8$ is $\_\_\_\_\_\_\_\_.$

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