
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
If $\left(2x-a\right)^{7}=a_{0}+a_{1}(x+1)+a_{2}(x+1)^{2}+a_{3}(x+1)^{3}+\ldots +a_{7}(x+1)^{7}$, and $a_{4}=-560$.<br/>$(1)$ Find the value of the real number $a$;<br/>$(2)$ Find the value of $|a_{1}|+|a_{2}|+|a_{3}|+\ldots +|a_{6}|+|a_{7}|$.

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