
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 $f(x) = 3^x - \frac {1}{3^{|x|}}$.
(1) If $f(x) = 2$, find the value of $x$.
(2) Determine the monotonicity of $f(x)$ when $x > 0$.
(3) If $3^t f(t) + mf(t) \geq 0$ holds for all $t \in \left[ \frac {1}{2}, 1 \right]$, find the range of the values for $m$.

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