
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
(1) $\left(\frac{9}{4}\right)^{\frac{1}{2}} - (-2009)^0 - \left(\frac{8}{27}\right)^{\frac{2}{3}} + \left(\frac{3}{2}\right)^{-2}$;  
(2) $\log_{25}625 + \lg 0.001 + \ln \sqrt{e} + 2^{-1+\log_{2}3}$.

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