
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 $n \geq 1$, the value of the expression 
\[(5^{n+1} + 6^{n+2})^2 - (5^{n+1} - 6^{n+2})^2\] is $k \cdot 30^{n+1}$ for some positive integer $k$. What is $k$?

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