
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

Determine the sum of the following series:

$$
s_{n} = 5^{2} + 2 \cdot 5^{2} \cdot 2 \cdot 3 + 3 \cdot 5^{2} \cdot 2^{2} \cdot 3^{2} + \ldots + n \cdot 5^{2} \cdot 2^{n-1} \cdot 3^{n-1}
$$

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