
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 that the domain of functions $f(x)$ and $g(x)$ is $R$, and they satisfy $f(x)-g(2-x)=4$, $g(x)+f(x-4)=6$, $g(3-x)+g(x+1)=0$, calculate $\sum_{n=1}^{30}{f(n)}$.

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