
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
Given that the time (in minutes) taken by a worker to assemble the x-th product is represented by the function $f(x) = \begin{cases} \frac{c}{\sqrt{x}}, & x < a\\ \frac{c}{\sqrt{a}}, & x \geqslant a \end{cases}$, and it is known that the worker took 30 minutes to assemble the 4th product and 5 minutes to assemble the a-th product, calculate the respective values of $c$ and $a$.

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