
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
The real numbers \( x, y, z, w \) satisfy
\[ 
\begin{array}{l} 
2x + y + z + w = 1 \\
x + 3y + z + w = 2 \\
x + y + 4z + w = 3 \\
x + y + z + 5w = 25 
\end{array}
\]

Find the value of \( w \).

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