
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

G8.1 The area of an equilateral triangle of side \( A \mathrm{~cm} \) is \( \sqrt{3} \mathrm{~cm}^{2} \). Find \( A \).

G8.2 If \( 19 \times 243^{\frac{A}{5}} = b \), find \( b \).

G8.3 The roots of the equation \( x^{3} - 173 x^{2} + 339 x + 513 = 0 \) are \( -1 \), \( b \), and \( c \). Find \( c \).

G8.4 The base of a triangular pyramid is an equilateral triangle of side \( 2 c \mathrm{~cm} \). If the height of the pyramid is \( \sqrt{27} \mathrm{~cm} \), and its volume is \( d \mathrm{~cm}^{3} \), find \( d \).

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