
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
Calculate:<br/>$(1)$ Factorize:<br/>① $5y-10y^{2}$;<br/>② $\left(3m-1\right)^{2}-9$;<br/>③ $a^{2}b-4ab+4b$.<br/>$(2)$ Solve the system of equations: $\left\{\begin{array}{l}{x-y=3}\\{x-3y=-1}\end{array}\right.$.

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