
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
Let proposition $p$: the inequality $a^{2}-5a-6 \gt 0$ holds true; proposition $q$: the equation $x^{2}+ax+1=0$ has two distinct negative roots for $x$.  
$(1)$ If proposition $p$ is true, find the range of real number $a$;  
$(2)$ If propositions "$p$ or $q$" is true, and "$p$ and $q$" are false, find the range of real number $a$.

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