
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 binomial expansion of ${(x+2\sqrt{2}a)^{4}}$ $(a > 0)$, the coefficient of ${x^{2}}$ is 75.

(1) Find the value of $a$;

(2) If the coefficient of ${x^{2}}$ in the binomial expansion of ${(x\sin \theta +1)^{5}}$ $(0 < \theta < \dfrac{\pi }{2})$ is equal to the coefficient of ${x^{3}}$ in the expansion of ${(x+a)^{4}}$, determine the value of $\theta$.

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