
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
Choose one of the following two conditions:①$\frac{sinA}{cosBcosC}=\frac{2{a}^{2}}{{a}^{2}+{c}^{2}-{b}^{2}}$, ②$sinB-cosB=\frac{\sqrt{2}b-a}{c}$, and complete the following questions:<br/>Let the sides opposite to the internal angles $A$, $B$, and $C$ of triangle $\triangle ABC$ be $a$, $b$, and $c$, respectively. Given that ___.<br/>$(1)$ Find the measure of angle $C$;<br/>$(2)$ If point $D$ lies on side $AB$ such that $BD=2AD$, $cosB=\frac{3}{5}$, find the value of $\tan \angle BCD$.

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