
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: $\log_{3}\left(\frac{427}{3}\right)+\lg 25+\lg 4+7^{\log_{7}2}+\log_{2}3 \cdot \log_{3}4$;  
Let set $A=\{x|\frac{1}{32} \leq 2^{-x} \leq 4\}$, set $B=\{x|m-1 < x < 2m+1\}$. If $A \cup B = A$, determine the range of values of $m$.

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