
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
Find all natural solutions to the inequality

$$
\frac{4}{5} + \frac{4}{45} + \frac{4}{117} + \cdots + \frac{4}{16n^{2} - 8n - 3} > n - 5
$$

In the response, write the sum of all the solutions found.

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