
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
In the diagram below, trapezoid $ABCD$ with $\overline{AB}\parallel \overline{CD}$ and $\overline{AC}\perp\overline{CD}$, it is given that $CD = 15$, $\tan C = 1.2$, and $\tan B = 1.8$. What is the length of $BC$?

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