
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 the function $f\left(x\right)=4^{x}+m\cdot 2^{x}$, where $m\in R$.  
$(1)$ If $m=-3$, solve the inequality $f\left(x\right) \gt 4$ with respect to $x$.  
$(2)$ If the minimum value of the function $y=f\left(x\right)+f\left(-x\right)$ is $-4$, find the value of $m$.

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