
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
\( w, x, y, z \) are real numbers such that
\[
\begin{aligned}
w+x+y+z & =5 \\
2 w+4 x+8 y+16 z & =7 \\
3 w+9 x+27 y+81 z & =11 \\
4 w+16 x+64 y+256 z & =1
\end{aligned}
\]
What is the value of \( 5w + 25x + 125y + 625z \)?

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