
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
What is the ratio of the area of the shaded square to the area of the large square in this new configuration? 

[asy]
size(1inch,1inch);
pair r1c1=(0,0), r1c2=(10,0), r1c3=(20,0), r1c4=(30,0), r1c5=(40,0), r1c6=(50,0);
pair r2c1=(0,10), r2c2=(10,10), r2c3=(20,10), r2c4=(30,10), r2c5=(40,10), r2c6=(50,10);
pair r3c1=(0,20), r3c2=(10,20), r3c3=(20,20), r3c4=(30,20), r3c5=(40,20), r3c6=(50,20);
pair r4c1=(0,30), r4c2=(10,30), r4c3=(20,30), r4c4=(30,30), r4c5=(40,30), r4c6=(50,30);
pair r5c1=(0,40), r5c2=(10,40), r5c3=(20,40), r5c4=(30,40), r5c5=(40,40), r5c6=(50,40);
pair r6c1=(0,50), r6c2=(10,50), r6c3=(20,50), r6c4=(30,50), r6c5=(40,50), r6c6=(50,50);
draw(r1c1--r1c6--r6c6--r6c1--cycle);
draw(r6c1--r4c3);
draw(r4c6--r2c6--r4c4);
fill(r3c3--r2c4--r3c5--r4c4--cycle);
[/asy]

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