
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 the Fibonacci sequence with  $f_0=f_1=1$ and for  $n\geq 1, f_{n+1}=f_n+f_{n-1}$ , find all real solutions to the equation:   $$ x^{2024}=f_{2023}x+f_{2022}. $$  

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