
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
Solve the equation \(2^{a+1} + 2^{a} + 2^{a-1} = 112\) for \(a\).

If \(a\) is one root of the equation \(x^{2} - b x + 35 = 0\), find \(b\).

If \(\sin \theta=\frac{-b}{15}\), where \(180^{\circ}<\theta<270^{\circ}\), and \(\tan \theta=\frac{c}{3}\), find \(c\).

The probability of getting a sum of \(c\) in throwing two dice is \(\frac{1}{d}\). Find \(d\).

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