
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
Find the conditional extremum of the function \( f(x_{1}, x_{2}) = x_{1}^{2} + x_{2}^{2} - x_{1} x - 2 + x_{1} + x_{2} - 4 \) subject to the constraint \( x_{1} + x_{2} + 3 = 0 \).

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