
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 $f(x)= \frac {9}{\sin^{2}x}+ \frac {4}{\cos^{2}x}$, where $x \in (0, \frac{\pi}{2})$, and $f(x) \geq t$ always holds.
(1) Find the maximum value of the real number $t$;
(2) When $t$ takes on the maximum value, find the solution set for the inequality $|x+ \frac{t}{5}|+|2x-1| \leq 6$.

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