
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
Simplify and evaluate the expression: $$(a+1- \frac {4a-5}{a-1})÷( \frac {1}{a}- \frac {1}{a^{2}-a})$$, where $a$ is a non-negative integer solution of the inequality system $$\begin{cases} 2x+1＜3x+3 \\ \frac {2}{3}(x-1)≤ \frac {1}{2}(x+ \frac {1}{3})\end{cases}$$.

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