
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 that the monotonically increasing function $f(x)$ defined on $\mathbb{R}$ is an odd function, and $f(x)= \sqrt {x}+1$ when $x > 0$.
(1) Find the value of $f(0)$ and the analytical expression of $f(x)$;
(2) If $f(k\cdot4^{x}-1) < f(3\cdot4^{x}-2^{x+1})$ holds for any $x\in\mathbb{R}$, find the range of values for the real number $k$.

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