
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
Suppose that  $ D,\ E$  are points on  $ AB,\ AC$  of  $ \triangle{ABC}$  with area  $ 1$  respectively and  $ P$  is  $ BE\cap CD$ . When  $ D,\ E$  move on  $ AB,\ AC$  with satisfying the condition  $ [BCED] \equal{} 2\triangle{PBC}$ , find the maximum area of  $ \triangle{PDE}$ .

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