
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
If \( x, y \), and \( z \) are real numbers such that \( 2 x^{2} + y^{2} + z^{2} = 2 x - 4 y + 2 xz - 5 \), find the maximum possible value of \( x - y + z \).

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