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

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