
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 $\left(1+mx\right)^{7}=a_{0}+a_{1}x+a_{2}x^{2}+\ldots +a_{7}x^{7}$, and $a_{3}=-280$.<br/>$(1)$ Find the value of $m$;<br/>$(2)$ Find the value of $a_{1}+a_{3}+a_{5}+a_{7}$.

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