
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 inequality $|t+3|-|t-2| \leq 6m-m^2$ holds for any $t \in \mathbb{R}$.

(Ⅰ) Find the range of values for the real number $m$;  
(Ⅱ) If the maximum value of the real number $m$ from (Ⅰ) is $\lambda$, and $3x+4y+5z=\lambda$, where $x$, $y$, $z \in \mathbb{R}$, find the minimum value of $x^2+y^2+z^2$.

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