
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
Solve the following system of equations over the real numbers: $2x_1 = x_5 ^2 - 23$  $4x_2 = x_1 ^2 + 7$  $6x_3 = x_2 ^2 + 14$  $8x_4 = x_3 ^2 + 23$  $10x_5 = x_4 ^2 + 34$ 

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