
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 set $M=\{m\in \mathbb{Z} | x^2+mx-36=0 \text{ has integer solutions}\}$, a non-empty set $A$ satisfies the conditions:  
(1) $A \subseteq M$,  
(2) If $a \in A$, then $-a \in A$, the number of all such sets $A$ is.

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