
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
Calculate the area of a triangle using logarithms, where the sides are: 
\[ a = 35.463 \,\text{m}, \quad b = 45.963 \,\text{m}, \quad c = 67.349 \,\text{m}. \]

Additionally, what is the side length of a square whose area is equal to the area of this triangle?

(The area of the triangle is \( t = \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{1}{2}(a+b+c) \).)

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