
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
In a factor tree, each value is the product of the two values below it unless the value is a prime number. Calculate the value of $A$ in the factor tree that includes an additional power operation in the top node:

[asy]
draw((-1,-.3)--(0,0)--(1,-.3),linewidth(1));
draw((-2,-1.3)--(-1.5,-.8)--(-1,-1.3),linewidth(1));
draw((1,-1.3)--(1.5,-.8)--(2,-1.3),linewidth(1));
label("A^2",(0,0),N);
label("B",(-1.5,-.8),N);
label("2",(-2,-1.3),S);
label("C",(1.5,-.8),N);
label("D",(-1,-1.3),S);
label("7",(1,-1.3),S);
label("E",(2,-1.3),S);
draw((-1.5,-2.3)--(-1,-1.8)--(-.5,-2.3),linewidth(1));
draw((1.5,-2.3)--(2,-1.8)--(2.5,-2.3),linewidth(1));
label("2",(-1.5,-2.3),S);
label("4",(-.5,-2.3),S);
label("7",(1.5,-2.3),S);
label("2",(2.5,-2.3),S);
[/asy]

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