
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 \( n \) be a positive integer. Calculate the following sum:

$$
\frac{3}{1 \cdot 2 \cdot 4 \cdot 5}+\frac{4}{2 \cdot 3 \cdot 5 \cdot 6}+\frac{5}{3 \cdot 4 \cdot 6 \cdot 7}+\ldots+\frac{n+2}{n \cdot(n+1) \cdot(n+3) \cdot(n+4)}
$$

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