
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
Given the sequence $\{a_n\}$ that satisfies $(2n+3)a_{n+1}-(2n+5)a_{n}=(2n+3)(2n+5)\lg (1+\frac{1}{n})$, and $a_{1}=5$, find the value of the $2016^{\text{th}}$ term of the sequence $\{ \frac{a_{n}}{2n+3} \}$.

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