
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
According to the given piecewise function $f(x)$, where $f(x) = \begin{cases} \frac{c}{\sqrt{x}}, & \text{if } x < m \\ \frac{c}{\sqrt{m}}, & \text{if } x \geq m \end{cases}$, it is known that it takes the worker 30 minutes to assemble the 4th product and 15 minutes to assemble the $m$-th product. Find the value of $m$.

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