
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
According to the graph, what is the average monthly balance, in dollars, of Lisa's savings account during the six-month period shown? Additionally, compute the average balance for the first three months and the last three months, then determine by how much the second average exceeds the first. [asy]
draw((0,0)--(15,0)--(15,12)--(0,12)--cycle,linewidth(1));
draw((0,3)--(15,3),linewidth(1));
draw((0,6)--(15,6),linewidth(1));
draw((0,9)--(15,9),linewidth(1));
draw((1,0)--(1,3)--(3,3)--(3,0)--cycle, linewidth(1));
fill((1,0)--(1,3)--(3,3)--(3,0)--cycle,lightgray);
draw((4,0)--(4,9)--(6,9)--(6,0)--cycle, linewidth(1));
fill((4,0)--(4,9)--(6,9)--(6,0)--cycle,lightgray);
draw((7,0)--(7,6)--(9,6)--(9,0)--cycle, linewidth(1));
fill((7,0)--(7,6)--(9,6)--(9,0)--cycle,lightgray);
draw((10,0)--(10,6)--(12,6)--(12,0)--cycle, linewidth(1));
fill((10,0)--(10,6)--(12,6)--(12,0)--cycle,lightgray);
draw((13,0)--(13,3)--(15,3)--(15,0)--cycle, linewidth(1));
fill((13,0)--(13,3)--(15,3)--(15,0)--cycle,lightgray);
label("J",(2,0),S);
label("F",(5,0),S);
label("M",(8,0),S);
label("A",(11,0),S);
label("M",(14,0),S);
label("J",(17,0),S);
label("100",(2,3),S);
label("300",(5,9),S);
label("200",(8,6),S);
label("200",(11,6),S);
label("100",(14,3),S);
label("100",(17,3),S);
label("100",(0,3),W);
label("200",(0,6),W);
label("300",(0,9),W);
label("400",(0,12),W);
label(rotate(90)*Label("Account Balance",(-5,6)));
label(rotate(90)*Label("(in dollars)",(-4,6)));
label("Lisa's Savings Account Balance",(7.5,14));
label("Month",(7.5,-3));
[/asy]

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