
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
Rose redesigns her rectangular flower bed with different dimensions for each region and different costs for flowers. The new lengths, in feet, of the rectangular regions in her flower bed are given in the diagram. Rose still plants one flower per square foot in each region. Asters now cost $1.20 each, begonias $1.80 each, cannas $2.20 each, dahlias $2.80 each, and Easter lilies $3.50 each. Furthermore, Rose aims to use no more than 50 flowers on dahlias due to budget constraints. What is the least possible cost, in dollars, for her garden?
[asy]
draw((0,0)--(12,0)--(12,7)--(0,7)--cycle,linewidth(0.7));
draw((0,2)--(7,2),linewidth(0.7));
draw((5,2)--(5,7),linewidth(0.7));
draw((7,0)--(7,4),linewidth(0.7));
draw((5,4)--(12,4),linewidth(0.7));
label("7",(3.5,0),S);
label("5",(9.5,0),S);
label("2",(0,1),W);
label("5",(0,4.5),W);
label("5",(2.5,7),N);
label("7",(8.5,7),N);
label("4",(12,3),E);
label("3",(12,5.5),E);
[/asy]

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