
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 functions \( f(x) \) and \( g(x) \) are defined for all \( x > 0 \). The function \( f(x) \) is equal to the greater of the numbers \( x \) and \( \frac{1}{x} \), and \( g(x) \) is equal to the smaller of the numbers \( x \) and \( \frac{1}{x} \). Solve the equation \( f(5x) \cdot g(8x) \cdot g(25x)=1 \). In the answer, specify the solution if it is unique, or the sum of the solutions if there are several. Round the answer to the nearest hundredth if necessary.

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