
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
Isosceles triangles $P$ and $P'$ have equal perimeters and areas. Triangle $P$ has side lengths 6, 6, and 10. Find the unique length $b$ for $P'$ if its sides are $c$, $c$, and $b$. Which of the following numbers is closest to $b$?
(Side lengths are given in centimeters and choices will be provided after solving.)
A) 4
B) 5
C) 6
D) 7
E) 8

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