
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 $f(x) = \frac{1}{2}x^2 - 2\ln{x} + a$ $(a \in R)$, $g(x) = -x^2 + 3x - 4$.
1. Find the monotonic intervals of $f(x)$;
2. Let $a = 0$, the lines $x = t$ intersect with the graphs of $f(x)$ and $g(x)$ at points $M$ and $N$, respectively. Find the value of $t$ when $|MN|$ reaches its minimum value.

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