
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) Calculate: $\log_{3} \frac{427}{3} + \lg 25 + \lg 4 + \log_{7}7^{2} + \log_{2}3 \cdot \log_{3}4$;

(2) Let set $A = \{x \mid \frac{1}{32} \leqslant 2^{-x} \leqslant 4\}$ and $B = \{x \mid m - 1 < x < 2m + 1\}$. If $A \cup B = A$, find the range of values for $m$.

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