
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
【Reading comprehension question】In mathematics, the method of using holistic thinking is very important in finding the value of algebraic expressions.<br/>For example: Given $a^{2}+2a=1$, then the algebraic expression $2a^{2}+4a+4=2(a^{2}+2a)+4=2\times 1+4=6$.<br/>Please answer the following questions based on the above material:<br/>$(1)$ If $x^{2}-3x=2$, find the value of $1+2x^{2}-6x$;<br/>$(2)$ If $x^{2}-3x-4=0$, find the value of $1+3x-x^{2}$;<br/>$(3)$ When $x=1$, the value of the algebraic expression $px^{3}+qx+1$ is $5$, find the value of the algebraic expression $px^{3}+qx+1$ when $x=-1$.

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