
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) There are 5 boys and 3 girls. If we select 5 people from them, and the condition is that there are only 2 girls, how many different arrangements are there when they stand in a line?

(2) From the set {-3,-2,-1,0,1,2,3,4}, choose three different elements as the coefficients of the quadratic function $y=ax^{2}+bx+c$. How many parabolas passing through the origin with the vertex in the first or third quadrant can be formed?

(3) Given $( \frac {1}{2}+2x)^{n}$, if the binomial coefficients of the 5th, 6th, and 7th terms in the expanded form are in arithmetic progression, find the binomial coefficient of the maximum term in the expansion.

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