
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 $S_n = 3 + 7 + 13 + \ldots + (2n + 2n - 1)$, and $S_{10} = a \cdot b \cdot c$, where $a, b, c \in \mathbb{N}^*$, the minimum value of $a + b + c$ is ______.

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