
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, define the function \( f(n) = \left\{ \begin{array}{l} 0, \text{ when } n \text{ is a perfect square, } \\ \left\lfloor \frac{1}{\{\sqrt{n}\}} \right\rfloor, \text{ when } n \text{ is not a perfect square, } \end{array} \right. \) where \( \lfloor x \rfloor \) 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