
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 triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Choose two conditions from ①, ②, and ③ below, supplement them into the following questions, and solve.<br/>① $\cos A = -\frac{17}{25}$; ② The area of $\triangle ABC$ is $\frac{6\sqrt{21}}{5}$; ③ $c = 3$.<br/>Given that angle $A$ is obtuse, $b = 5$, _____.<br/>$(1)$ Find the area of the circumcircle of $\triangle ABC$;<br/>$(2)$ $AD$ is the bisector of angle $A$, $D$ lies on $BC$, find the length of $AD$.

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