
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
Given the exponential function $y=g(x)$ satisfies $g(3)=27$, and the function $f(x)=\frac{\mathbf{n{-}g(x)}}{\mathbf{m{+}3}\mathbf{g(x)}}$ with domain $R$ is an odd function.

(1) Determine the analytical expressions for $y=g(x)$ and $y=f(x)$;

(2) If for any $t∈(1,4)$, the inequality $f(2t-3)+f(t-k) > 0$ always holds, find the range of values for the real number $k$.

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