
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
Solve the equations:

(1) $3x-2=10-2(x+1)$;

(2) $\frac{2x+1}{3}-\frac{5x-1}{6}=1$;

(3) $\begin{cases} x+2y=5 \\ 3x-2y=-1 \end{cases}$;

(4) $\begin{cases} 2x+y+z=15 \\ x+2y+z=16 \\ x+y+2z=17 \end{cases}$.

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