
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 the staircase-shaped region below, all angles that look like right angles are right angles, and each of the ten congruent sides marked with a tick mark have length 2 feet. Additionally, a right triangle with legs of 3 feet and 4 feet is adjoined at one end. If the region has an area of 150 square feet, what is the number of feet in the perimeter of the region?
[asy]
size(150);
draw((8,10)--(0,10)--(0,0)--(13,0)--(13,4)--(11,4)--(11,6)--(9,6)--(9,8)--(7,8)--(7,10)--cycle);
label("13 ft",(6.5,0),S);
draw((10.9,5)--(11.1,5)); draw((8.9,7)--(9.1,7));
draw((10.5,3.9)--(10.5,4.1)); draw((8.5,5.9)--(8.5,6.1));
draw((6.5,7.9)--(6.5,8.1)); draw((7.9,9)--(8.1,9));
draw((0,10)--(3,10)--(0,7)--cycle, blue+dashed);
[/asy]

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