
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 $f(x)=x^2+px+q$ and $g(x)=x+ \frac {4}{x}$ are functions defined on the set $A=\{x|1\leq x\leq \frac {5}{2}\}$, for any $x\in A$, there exists a constant $x_0 \in A$ such that $f(x) \geq f(x_0)$, $g(x) \geq g(x_0)$ and $f(x_0)=g(x_0)$. The maximum value of $f(x)$ on set $A$ is:
A) $\frac {5}{2}$
B) $\frac {17}{4}$
C) 5
D) $\frac {41}{10}$

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