
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
Find all non-negative integer solutions \((x, y, z, w)\) to the equation
\[ 
2^{x} \cdot 3^{y} - 5^{z} \cdot 7^{w} = 1.
\]

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