
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
Suppose $x$, $y$, $z$, and $w$ are integers satisfying:
1. $x - y + z = 7$,
2. $y - z + w = 8$,
3. $z - w + x = 4$,
4. $w - x + y = 3$.
What is the value of $x + y + z + w$?

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