
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
The line $y = b-x$ with $0 < b < 6$ intersects the $y$-axis at $P$ and the line $x=6$ at $S$. If the ratio of the area of triangle $QRS$ to the area of triangle $QOP$ is 4:25, what is the value of $b$? Express the answer as a decimal to the nearest tenth.

[asy]
draw((0,-3)--(0,5.5),Arrows);
draw((6,-3.5)--(6,5),Arrows);

draw((-2,0)--(8,0),Arrows);

draw((-2,6.5)--(8,-4.5),Arrows);

dot((0,0));
dot((3,0));
dot((6,0));
dot((6,-3));
dot((0,3));

label("O",(0,0),SW);
label("P",(0,3),NE);
label("Q",(3,0),NE);
label("R",(6,0),NE);
label("S",(6,-3),SW);

label("$y$-axis",(0,5.5),N);
label("$x=6$",(6,5),N);
label("$x$-axis",(8,0),E);
label("$y=b-x$",(8,-4.5),SE);
[/asy]

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