
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 volume of a hemisphere with diameter \(a \, \text{cm}\) is \(18 \pi \, \text{cm}^{3}\), find \(a\).

If \(\sin 10 a^{\circ} = \cos \left(360^{\circ} - b^{\circ} \right)\) and \(0 < b < 90\), find \(b\).

The triangle is formed by the \(x\)-axis and \(y\)-axis and the line \(b x + 2 b y = 120\). If the bounded area of the triangle is \(c\), find \(c\).

If the difference of the two roots of the equation \(x^{2} - (c + 2)x + (c + 1) = 0\) is \(d\), find \(d\).

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