
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
Let $f(x) = \log(5-x)$.
(1) If $10^{f(k)} = 10^{f(2)} \cdot 10^{f(3)}$, find the value of $k$;
(2) If $f(2m-1) < f(m+1)$, find the range of the real number $m$.

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