
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
Real numbers  $a$  and  $b$  satisfy the system of equations   $$ \begin{cases} a^3-a^2+a-5=0  b^3-2b^2+2b+4=0  \end{cases} $$    Find the numerical value of the sum  $a+ b$ .

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