
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
Let \(\lfloor x \rfloor\) denote the greatest integer less than or equal to \(x\). If \(a_{n} \lfloor a_{n} \rfloor = 49^{n} + 2n + 1\), find the value of \(2S + 1\), where \(S = \left\lfloor \sum_{n=1}^{2017} \frac{a_{n}}{2} \right\rfloor\).

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