
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 following systems of equations:

(1)
\begin{cases}
2x + y = 4 \
x + 2y = 5
\end{cases}

(2)
\begin{cases}
x + y = 9 \
3(x + y) + 2x = 33
\end{cases}

(3)
\begin{cases}
2x + 3y = 12 \
3x - 2y = 5
\end{cases}

(4)
\begin{cases}
\frac{x}{2} - \frac{y+1}{3} = 1 \
3x + 2y = 10
\end{cases}

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