
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
Carefully read the following example and answer the questions:<br/>Example: Given the quadratic trinomial $x^{2}-4x+m$ has a factor of $\left(x+3\right)$, find the other factor and the value of $m$.<br/>Solution: Let the other factor be $\left(x+n\right)$, we have<br/>$x^{2}-4x+m=\left(x+3\right)\left(x+n\right)$,<br/>then $x^{2}-4x+m=x^{2}+\left(n+3\right)x+3n$,<br/>$\therefore \left\{\begin{array}{l}{n+3=-4}\\{m=3n}\end{array}\right.$.<br/>Solving gives: $n=-7$, $m=-21$.<br/>$\therefore $ the other factor is $\left(x-7\right)$, and the value of $m$ is $-21$.<br/>Question:<br/>$(1)$ Given the quadratic trinomial $x^{2}+6x+a$ has a factor of $\left(x+5\right)$, find the other factor and the value of $a$;<br/>$(2)$ Given the quadratic trinomial $6x^{2}-x-p$ has a factor of $\left(2x+3\right)$, find the other factor and the value of $p$.

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