
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 $f(x)$ be an odd function defined on the real number set $\mathbb{R}$ with the smallest positive period of 2, and when $x \in (0,1)$, $$f(x)= \frac {2^{x}}{4^{x}+1}.$$  
(Ⅰ) Find the analytic expression of $f(x)$ on $(-1,1)$.  
(Ⅱ) Determine the monotonicity of $f(x)$ on $(0,1)$.  
(Ⅲ) For what value of $\lambda$ does the equation $f(x)=\lambda$ have a real solution on $(-1,1)$?

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