
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 $f(x) = 2x^2 + bx + c$, the solution set of the inequality $f(x) < 0$ is $(0,5)$,
$(1)$ Find the explicit form of $f(x)$;
$(2)$ If the inequality $f(x) + t \leq 2$ holds true for any $x \in [-1,1]$, find the range of values for $t$.

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