
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
Let \( y \) be the time after which the motorcyclist started riding following the departure of the cyclist. The speeds of the cyclist and the motorcyclist are \( V_B = x \) km/h and \( V_M = 50 \) km/h respectively.

Find the value of \( x \) using the following system of equations:

\[
\left\{\begin{array}{c}
\frac{20}{x} - \frac{20}{50} = y \\
70 - \frac{8}{3} x = 50 \left( \frac{7}{15} - y \right)
\end{array}\right.
\]

Solving the above equations will yield \( x = 25 \) km/h.

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