
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  $a$  be a real number, define functions  $f(x),\ g(x)$  defined on  $x>0$  as follows.
\[f(x)=\frac{\cos x}{x}\]
\[g(x)=\sin x+ax\]

Find all possible  $a$  such that graphs of  $y=f(x)$  and  $y=g(x)$  intersect exactly three points on  $x>0$ .

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