
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 $0 \leqslant x \leqslant 1$, find the range of real number $t$ for which the equation $f(x) + 1 = t$ has a solution in terms of $x$.

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