
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
1. In $\triangle ABC$, if $b=5$, $\angle B= \frac{\pi}{4}$, $\sin A= \frac{1}{3}$, then $a=$\_\_\_\_.
2. Given sets $A=\{x\in R|3x+2 > 0\}$, $B=\{x\in R|(x+1)(x-3) > 0\}$, then $A\cap B=$\_\_\_\_.
3. If the sequence $\{a\_n\}$ satisfies: $a\_1=1$, $a\_{n+1}=2a\_n, n=1, 2, 3…$, then $a\_1+a\_2+…+a\_n=$\_\_\_\_.
4. Given $m > 0$, $n > 0$, $2m+n=4$, then the minimum value of $\frac{1}{m} + \frac{2}{n}$ is \_\_\_\_.

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