
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 equations using appropriate methods:  
(1) $3x(x-1)=1-x$  
(2) $(x+3)(1-3x)=5+x^2$  
(3) $25(x-2)^2-4(2x+3)^2=0$  
(4) $2x^2-|x|-6=0$．

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