
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
A student was given a math problem: "Given two polynomials $A$ and $B$, where $B = 4x^{2}-5x-7$, find the value of $A+2B$." Xiao Li mistakenly calculated $A+2B$ as $A-2B$, and obtained the result $-2x^{2}+10x+14$. <br/>$(1)$ Find the polynomial $A$; <br/>$(2)$ Find the value of $A+2B$ when $x=-1$.

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