
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
By adding the second and third equations to the first equation, we obtain:

\[ x^{2}+2x+y^{2}+4y+z^{2}+6z=-14 \]

Next, complete the square for each variable. As a result, we obtain:

\[ (x+1)^{2}+(y+2)^{2}+(z+3)^{2}=0 \]

Therefore, \( x=-1 \), \( y=-2 \), and \( z=-3 \) is the only possible solution. It remains to verify this by substituting these values into the second and third equations of the system.

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