
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
Let \( x = 19.\overline{87} \). If \( 19.\overline{87} = \frac{a}{99} \), find \( a \).

If \( \frac{\sqrt{3}}{b \sqrt{7} - \sqrt{3}} = \frac{2 \sqrt{21} + 3}{c} \), find \( c \).

If \( f(y) = 4 \sin y^{\circ} \) and \( f(a - 18) = b \), find \( b \).

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