
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
For each positive integer \( n \), define the function
\[ f(n) = \begin{cases} 
0, & \text{if } n \text{ is a perfect square} \\ 
\left\lfloor \frac{1}{\{\sqrt{n}\}} \right\rfloor, & \text{if } n \text{ is not a perfect square} 
\end{cases} \]
(where \( \left\lfloor x \right\rfloor \) denotes the greatest integer less than or equal to \( x \), and \( \{x\} = x - \lfloor x \rfloor \)).

Find the value of \( \sum_{k=1}^{240} f(k) \).

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