
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 $f(x)= \begin{cases} 3^{|x-4|},x\neq 4 \\ 2,x=4 \end{cases}$, find the value of $h(x_{1}+x_{2}+x_{3}+x_{4}+x_{5})$ where $x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, $x_{5}$ are the distinct real roots of the equation $f^{2}(x)+bf(x)+c=0$ in terms of $x$.

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