
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
Observe that $7 = 5 \times 1 + 2$, $12 = 5 \times 2 + 2$, and $17 = 5 \times 3 + 2$. Here, 7, 12, and 17 are called "3 consecutive numbers that leave a remainder of 2 when divided by 5." If the sum of 3 consecutive numbers that leave a remainder of 2 when divided by 5 is equal to 336, find the smallest of these numbers.

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