
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 $f(x) = \sqrt{10\sin x - 2} - \sqrt{5\cos x - 3}$.

(1) If acute angle $\theta$ satisfies $\tan 2\theta = \frac{24}{7}$, is $\theta$ a solution to the equation $f(x) = 1$? Why?

(2) Find the solution set of the equation $f(x) = 1$ in the interval $(-\infty, +\infty)$.

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