
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 $y=x+ \frac {a}{x}$, it has the following properties: If the constant $a>0$, then the function is decreasing on $(0, \sqrt {a}]$ and increasing on $[\sqrt {a}, +\infty)$.  
(1) If the function $y=x+ \frac {3^{b}}{x}$ ($x>0$) is decreasing on $(0,3]$ and increasing on $[3, +\infty)$, find the value of $b$;  
(2) Let the constant $c\in[1,4]$, find the maximum and minimum values of the function $f(x)=x+ \frac {c}{x}$ ($1\leq x\leq 2$).

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