
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 equations:<br/>
$(1) 4x = 2x + 6$;<br/>
$(2) 3x + 5 = 6x - 1$;<br/>
$(3) 3x - 2(x-1) = 2 + 3(4-x)$;<br/>
$(4) \frac{x-3}{5} - \frac{x+4}{2} = -2$.

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