
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 a basketball player has a probability of $a$ for scoring 3 points in a shot, $b$ for scoring 2 points, and $c$ for not scoring any points, where $a, b, c \in (0, 1)$, and the mathematical expectation for scoring points in one shot is 2, determine the minimum value of $\frac{2}{a} + \frac{1}{3b}$.

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