
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 function $$f(x)= \frac {2}{3^{x}+1}+a(a\in\mathbb{R})$$ is an odd function,
(1) Find the value of $a$;
(2) When $0\leq x\leq 1$, the equation $f(x)+1=t$ has a solution, find the range of the real number $t$;
(3) Solve the inequality $f(x^2-mx)\geq f(2x-2m)$.

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