
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 $f(x)=\left\{{\begin{array}{l}{3x+1, x<3}\\{{x^2}-αx, x\geq3}\end{array}}\right.$, if $f({f({\frac{2}{3}})})=3$, then the real number $a=\_\_\_\_\_\_$.

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