
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  $a,b$  be the smaller sides of a right triangle. Let  $c$  be the hypothenuse and  $h$  be the altitude from the right angle. Fint the maximal value of  $\frac{c+h}{a+b}$ .

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