
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 $f(x) = |x-1| + |2x+3|$, where $x \in \mathbb{R}$,

(Ⅰ) Find the minimum value $m$ of the function $f(x)$;

(Ⅱ) If $a, b, c \in \mathbb{R}$, and $a^4 + b^4 + c^4 = m$, find the maximum value of $a^2 + 2b^2 + 3c^2$.

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