
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
The binomial coefficient of the third term in the binomial expansion of ${(1-3x)^{n}}$ is equal to the binomial coefficient of the fifth term.

(1) Find $n$; (2) Find the coefficient of the fourth term;
(3) If ${(1-3x)^{n}={a_{0}}+{a_{1}}x+ \cdots +{a_{n}}x^{n}}$, find:
①${{a_{1}}+{a_{2}}+ \cdots +{a_{n}}}$;
②${{a_{0}}+{a_{2}}+{a_{4}}+ \cdots }$;
③${|{a_{0}}|+|{a_{1}}|+ \cdots +|{a_{n}}|}$.

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