
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
Let $a$ and $b$ both represent rational numbers. A new operation "$\triangle$" is defined as follows: when $a \geq b$, $a\triangle b = b^{2}$; when $a < b$, $a\triangle b = 2a - b$. For example, $1\triangle 2 = 2 \times 1 - 2$, $3\triangle (-2) = (-2)^{2} = 4$. Find the value of:

$(1)$ $\left(-3\right)\triangle \left(-4\right)$;

$(2)$ $\left(-2\triangle 3\right)\triangle \left(-8\right)$.

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