
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
Read the following material and answer the questions below.  
Material: From the meaning of exponentiation, we have $10^{2}\times 10^{3}=10\times 10\times 10\times 10\times 10=10^{5}$,  
$(-2)^{3}\times \left(-2\right)^{4}=\left(-2\right)\times \left(-2\right)\times \left(-2\right)\times \left(-2\right)\times \left(-2\right)\times \left(-2\right)\times \left(-2\right)=\left(-2\right)^{7}$.  
Thus, we can obtain the operation rule of multiplication of powers with the same base: $a^{m}\cdot a^{n}=a^{m+n}$ (where $m$ and $n$ are positive integers).  
Questions:  
$(1)$ Calculate:  
① $(-\frac{1}{2})^4×(-\frac{1}{2})^6$;  
② $3^{2}\times \left(-3\right)^{3}$.  
$(2)$ Write $2^{3}+2^{3}+2^{3}+2^{3}$ in the form of a power with base 2.  
$(3)$ If $\left(x-y\right)^{2}\cdot \left(x-y\right)^{p}\cdot \left(x-y\right)^{5}=\left(x-y\right)^{2023}$, find the value of $p$.

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