
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
Define a new operation, observe the following expressions:  
$1\odot 3=1\times 2+3=5$, $4\odot \left(-1\right)=4\times 2-1=7$;  
$(-2)\odot 3=\left(-2\right)\times 2+3=-1$; $6\odot 5=6\times 2+5=17$; $\ldots$  
$(1)$ Please think about: Express $x\odot y$ with an algebraic expression as ______;  
$(2)$ If $a\odot \left(-6b\right)=4$, calculate the value of $\left(a-5b\right)\odot \left(a+b\right)$.

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