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

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