
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  $a,b,c$  with  $a\neq b$  verify   $$ a^2(b+c)=b^2(c+a)=2023. $$   Find the numerical value of  $E=c^2(a+b)$ .

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