
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 $f\left( x \right)=\lg \left( \sqrt{1+{{x}^{2}}}-x \right)-{{x}^{3}}$, $x∈R$, if $\theta \in \left[ 0,\dfrac{\pi }{2} \right]$ and the inequality $f(\cos ^{2}\theta-2t)+f(4\sin \theta-3)\geqslant 0$ always holds, determine the range of values for the real number $t$.

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