
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 that $3^7 \cdot 5^3 = a^b$, where $a$ and $b$ are positive integers, find the smallest possible value for $a+b$.
- **A)** 273376
- **B)** 3376
- **C)** 40000
- **D)** 273400

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