
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
(I) Given the functions $f(x) = |x+3|$ and $g(x) = m-2|x-11|$, if $2f(x) \ge g(x+4)$ always holds, find the range of the real number $m$.  
(II) Given real numbers $x$, $y$, $z$ satisfying $2x^2+3y^2+6z^2=a$ ($a>0$) and the maximum value of $x+y+z$ is 1, find the value of $a$.

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