
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 $(1)\ (3x-1)^{4}=a\_{0}+a\_{1}x+a\_{2}x^{2}+a\_{3}x^{3}+a\_{4}x^{4}$.

$(①)$ Find $a\_{0}+a\_{1}+a\_{2}+a\_{3}+a\_{4}$;
$(②)$ Find $a\_{0}+a\_{2}+a\_{4}$;
$(③)$ Find $a\_{1}+a\_{2}+a\_{3}+a\_{4}$;

$(2)$ Find the remainder when $S=C\_{27}^{1} +C\_{27}^{2} +…+C\_{27}^{27}$ is divided by $9$.

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