
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 that $x=2$ is a solution to the equation $ax+b=c$ with respect to $x$. Find:

$(1)$ $\left(2a+b-c-1\right)^{2023}$;

$(2)$ The value of $\frac{10c}{4a+2b}$;

$(3)$ Solve the equation with respect to $x$: $\left(2a+b\right)x=c+4a+2b$ ($c\neq 0$).

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