
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
Calculate:

(1) Solve the equation: $2x^{2}-4x-6=0$;

(2) Solve the equation: $(x-2)^{2}=8-x$;

(3) $\sqrt { \frac {25}{9}}+(\frac {27}{64})\,^{- \frac {1}{3}}-π^{0}$;

(4) $\lg \frac {1}{2}-\lg \frac {5}{8}+\lg 12.5-\log _{8}9\cdot\log _{9}8.$

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