
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 polynomial $f(x)=2x^6-5x^4-4x^3+3x^2-6x$, calculate its value at $x=5$ using the Horner's method. If $a+b=v_2$, where $v_2=\_\_\_\_\_\_\_\_\_\_\_\_$, and $a>0$, $b>0$, then the minimum value of $\frac {1}{a}+ \frac {4}{b}$ is $\_\_\_\_\_\_\_\_\_\_\_\_$.

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