
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 circles $C\_1$: $x^{2}+y^{2}=4$ and $C\_2$: $(x-2)^{2}+(y-2)^{2}=4$, if point $P(a,b)(a > 0,b > 0)$ is on the common chord of the two circles, then the minimum value of $\frac {1}{a}+ \frac {9}{b}$ is \_\_\_\_\_\_.

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