
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
Define the function \( f(k) \) as follows:
\[ f(k)=\begin{cases} 
0, & k \text{ is a perfect square} \\ 
\left\lfloor \frac{1}{\{\sqrt{k}\}} \right\rfloor, & k \text{ is not a perfect square}
\end{cases} \]
Compute \( \sum_{k=1}^{240} f(k) \).

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