
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
For $c > 0$, given that nonzero real numbers $a$ and $b$ satisfy $a^{2}-2ab+2b^{2}-c=0$ and maximize the expression $a+b$, determine the minimum value of $\frac {3}{a}- \frac {4}{b}+ \frac {5}{c}$.

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