
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 $a > b > 0$, if $7a^2 + 8ab + 4b^2 = 24$, find the value of $b$ when $3a + 2b$ is at its maximum. If $\frac{1}{a - b} + \frac{1}{b} = 1$, find the minimum value of $a + 3b$.

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