
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
Given the sets $A=\{-4,2a-1,a^{2}\}$ and $B=\{a-5,1-a,9\}$, find the values of $a$ that satisfy the following conditions:
$(1) 9 \in (A \cap B)$;
$(2) \{9\} = A \cap B$.

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