
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 any positive integer n, let $f(n) = \left\{\begin{matrix} \log_{4}{n}, & \text{if } \log_{4}{n} \text{ is rational,} \\ 0, & \text{otherwise.} \end{matrix}\right.$ Calculate the sum of f(n) for n = 1 to 4095.

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